Ralf Schindler

 

Full Professor (C4) of Set Theory

Institut für mathematische Logik und Grundlagenforschung

Fachbereich Mathematik und Informatik

Universität Münster

Einsteinstr. 62

48149 Münster, F.R.G.

e-mail: rds at uni-muenster dot de

(with the "at" replaced by "@," and the "dot" replaced by a dot)

phone: +49-251-83-33790 or +49-251-83-33761

fax: +49-251-83-33078

Erdös #: 2; Research interest: set theory.

Sprechstunde: n.V. und per zoom

 

Contents: Publications, Manuscript by Ronald Jensen on fine structure, inner model theory, and the core model below one Woodin cardinal, version as of March 19, 2024, scripts + Übungszettel zur VL "Logik 1" im SoSe 2020, Notes and preprints, Service activities, Ph.D. students, Talks, Reviews, CV, some pictures, pictures of set theorists riding the logic bike.

Publications

See also here.


Books:

  1. Logische Grundlagen der Mathematik, Springer--Verlag 2009.
  2. Set theory. Exploring independence and truth, 332+x pp., Springer--Verlag 2014. You may order it here or here. Here is Schindler's list of errata, updated on Jan 26, 2021.
  3. (with John Steel) The core model induction (version as of April 12, 2013, with a correct proof of the existence of A-iterable mice): PDF.
  4. (with Mateo Wuttig, Luisa Degen, Alissa Fock, Yorick Fuhrmann, Lena Heidenreich, Alea Hofstetter, Kai Käfer, Tessa Kammermeier, Ingmar Kindermann, Linus Kulmann, Lisa Laun, Sandra Müller, Paul Stephan, Klaus Stier, and Todor Stoyanov) To Infinity and Beyond. The Continuum Problem in Modern Set Theory , actively written .


Research papers:

  1. Prädikative Klassen, Erkenntnis 39 (1993), pp. 209–241.
  2. A Dilemma in the Philosophy of Set Theory, Notre Dame Journal of Formal Logic 35 (1994), pp. 458–463. PDF
  3. Weak Covering at Large Cardinals, Mathematical Logic Quarterly 43 (1997), pp. 22–28.
  4. On a Chang Conjecture, Israel Journal of Mathematics 99 (1997), pp. 221–230.
  5. The core model up to one strong cardinal, Bonner Mathematische Schriften Nr. 295 (1997).
  6. On a Chang Conjecture II, Archive for Mathematical Logic 37 (1998), pp. 215–220.
  7. Successive weakly compact or singular cardinals, Journal of Symb. Logic 64 (1999), pp. 139–146.
  8. Weak covering and the tree property, Archive for Mathematatical Logic 38 (1999), pp. 515–520.
  9. (joint with M. Foreman and M. Magidor) The consistency strength of successive cardinals with the tree property, Journal of Symbolic Logic 66 (2001), pp. 1837–1847.
  10. (joint with K. Hauser) Projective uniformization revisited, Annals of Pure and Appl. Logic 103 (2000), pp. 109–153. PS. PDF by sciencedirect.
  11. Strong cardinals and sets of reals in L_{\omega_1}(R), Mathematical Logic Quarterly 45 (1999), pp. 361–369. PDF.
  12. Coding into K by reasonable forcing, Transactions of the Amer. Math. Soc 353 (2000), pp. 479 - 489. PS.
  13. (joint with S. Friedman) Universally Baire sets and definable well-orderings of the reals, Journal of Symbolic Logic 68 (2003), pp. 1065 - 1081. PS, PDF.
  14. (joint with J. Steel and M. Zeman) Deconstructing inner model theory, Journal of Symbolic Logic 67 (2002), pp. 721 - 736. PS, PDF.
  15. Proper forcing and remarkable cardinals, Bulletin of Symbolic Logic 6 (2000), pp. 176 - 184. PS, PDF.
  16. Proper forcing and remarkable cardinals II, Journal of Symbolic Logic 66 (2001), pp. 1481- 1492. PS, PDF.
  17. The core model for almost linear iterations, Annals of Pure and Appl. Logic 116 (2002), pp. 207 - 274. PS, PDF, PDF by sciencedirect.
  18. Iterates of the core model, Journal of Symbolic Logic 71 (2006), pp.241-251. PS, PDF.
  19. Mutual stationarity in the core model, Proceedings of LC2001, in: "Logic colloquium 01" (Baaz et al., eds., Lecture Notes in Logic 20, 2005), pp.386-401. PS, PDF.
  20. (joint with Th. Räsch) A new condensation principle, Archive for Math. Logic 44 (2005), pp.159-166. PS, PDF.
  21. Forcing axioms and projective sets of reals, Proceedings of FotFS III, in: "Classical and new paradigms of computation and their complexity hierarchies" (Löwe et al., eds., Kluwer 2004), pp.207-222. PS, PDF.
  22. P ≠ NP for infinite time Turing machines, Monatshefte für Mathematik 139 (4) (2003), pp.335-340. PS, PDF. PDF by Springer.
  23. (joint with B. Mitchell) A universal extender model without large cardinals in V, J. Symb. Logic 69 (2004), pp. 371-386. PS.
  24. (joint with M. Gitik and S. Shelah), Pcf theory and Woodin cardinals, Proceedings of LC2002 (Chatzidakis et al., eds.), Lecture Notes in Logic 27, pp. 172-205. PS, PDF.
  25. (joint with P. Koepke) Homogeneously Souslin sets in small inner models, Archive for Math. Logic 45 (2006), pp.53-61. PS, PDF.
  26. (joint with J. Hamkins and V. Deolalikar) P ≠ NP ∩ coNP for infinite time Turing machines, Journal of Logic and Computation 15 (2005), pp. 577-592. PS.
  27. (joint with M. Zeman) Fine structure theory, a chapter for the Handbook of Set Theory (Foreman, Kanamori, Magidor, eds.), Springer-Verlag 2009. PS, PDF. Here is a complete proof of Lemma 6.8.
  28. Semi-proper forcing, remarkable cardinals, and Bounded Martin's Maximum, Mathematical Logic Quarterly 50 (6) (2004), pp. 527 - 532. PS, PDF.
  29. Bounded Martin's Maximum and strong cardinals, in: Set theory. Centre de recerca Matematica, Barcelona 2003-4 (Bagaria, Todorcevic, eds.), Basel 2006, pp. 401-406. PS, PDF.
  30. (with A. Caicedo) Projective well-orderings of the reals, Archive for Mathematical Logic 45 (2006), pp. 783-794. PS
  31. Core models in the presence of Woodin cardinals, J. Symb. Logic 71 (2006), pp. 1145-1154. PS, PDF.
  32. (with J. Steel) The self-iterability of L[E], Journal of Symb. Logic 74 (2009), pp. 751-779. PS, PDF.
  33. (with G. Fuchs and I. Neeman) A criterion for coarse iterability, Archive Math. Logic 49 (2010), pp. 447-468. PDF.
  34. (with R. Jensen, E. Schimmerling, and J. Steel) Stacking mice, Journal of Symb. Logic 74 (2009), pp.315-335. PS, PDF.
  35. (with B. Claverie) Increasing u2 by a stationary set preserving forcing, Journal of Symb. Logic 74 (2009), pp.187-200. PS, PDF.
  36. (with D. Busche) The strength of choiceless patterns of singular and weakly compact cardinals, Ann. Pure Appl. Logic, 159 (2009), pp. 198-248. PDF.
  37. (with P. Schlicht) Thin equivalence relations in scaled pointclasses, Mathematical Logic Quarterly 57, 6 (2011), pp. 615 -- 620. PDF
  38. (with P. Doebler) Π2 consequences of BMM plus NS is precipitous and the semiproperness of all stationary set preserving forcings, Math. Res. Letters 16 (2009), no. 5, pp. 797 -- 815. PDF.
  39. (with B. Claverie) Woodin's axiom (*), bounded forcing axioms, and precipitous ideals on \omega_1, Jornal of Symbolic Logic 77 (2014), pp. 475 -- 498. PDF
  40. (with G. Fuchs) Inner model theoretic geology, Journal Symb. Logic, Volume 81, Issue 3, September 2016, pp. 972-996. PDF
  41. (with P. Doebler) The extender algebra and vagaries of Σ21 absoluteness, Münster Journal of Mathematics 6 (2013), pp. 117 - 166. PDF
  42. (with A. Caicedo, G. Sargsyan, P. Larson, J. Steel, and M. Zeman) Square principles in Pmax extensions, Israel J. of Mathematics 217 (2017), pp. 231-261. PDF
  43. (with D. Asperó) Bounded Martin's Maximum with an asterisk, Notre Dame J. Formal Logic 55 (2014), pp. 333--348. PDF
  44. (with C. Yong) Harrington's principle in higher order arithmetic, Journal of Symbolic Logic 80, Issue 2 (June 2015), pp. 477-489. PDF
  45. (with T. Hofweber) Hyperreal-valued probability measures approximating a real-valued measure, Notre Dame J. of Formal Logic, Volume 57, Number 3 (2016), pp. 369-374. PDF
  46. Remarkable cardinals, in: Infinity, Computability, and Metamathematics (Geschke et al., eds.), Festschrift celebrating the 60th birthdays of Peter Koepke and Philip Welch, pp. 299-308. PDF
  47. (with S. Müller and W.H. Woodin) Mice with finitely many Woodin cardinals from optimal determinacy hypotheses, Journal of Mathematical Logic, accepted to appear. PDF
  48. (with S. Friedman and D. Schrittesser) Coding over core models, in: Infinity, Computability, and Metamathematics (Geschke et al., eds.), Festschrift celebrating the 60th birthdays of Peter Koepke and Philip Welch, pp. 167-182. PDF
  49. Woodin's axiom (*), or Martin's Maximum, or both?, in: Foundations of mathematics, essays in honor of W. Hugh Woodin's 60th birthday, Harvard University (Caicedo et al., eds.), 177-204. PDF
  50. (with 's. Rinot) Square with built-in diamond-plus, J. Symb. Logic, Volume 82, Issue 3  September 2017, pp. 809-833. PDF
  51. (with J. Bagaria and V. Gitman) Remarkable cardinals, structural reflection, and the weak Proper Forcing Axiom, Archive for Math. Logic, Volume 56, Issue 1-2, 2017, pp. 1-20. PDF
  52. (with Ph. Lücke and Ph. Schlicht) Lightface definable subsets of Hω2, Journal Symb. Logic, Volume 82, Issue 3, September 2017, pp. 1106-1131. PDF
  53. (with G. Fuchs) The solidity and non--solidity of initial segments of the core model, Journal of Symb. Logic 83(3), 2018, pp. 920-938. PDF
  54. (with G. Sargsyan) Varsovian models I, Journal of Symb. Logic 83 (2018), pp. 496-528. PDF
  55. (with G. Sargsyan and F. Schlutzenberg) Varsovian models II, submitted. pdf
  56. The long extender algebra, Archive for Math. Logic 2018, Volume 57, Issue 1-2, pp 73-82. PDF
  57. (with M. Beriashvili, L. Wu, and L. Yu) Hamel bases and well-ordering the continuum, Proc. Amer. Math. Soc. 146 (2018), pp. 3565-3573. PDF.
  58. (with T. Wilson) Universally Baire sets of reals and the perfect set property, pdf, Journal Symb. Logic, submitted.
  59. (with J. Brendle, F. Castiblanco, L. Wu, and L. Yu) A model with everything except for a well-ordering of the reals, pdf, Fund. Math., submitted. There is a video of a talk by F. Castiblanco on this on youtube!
  60. (with V. Gitman) Virtual large cardinals, pdf, LC 2015 proceedings volume (Åsa Hirvonen, Thomas Scanlon, Jouko Väänänen, Dag Westerståhl, eds.), Annals of Pure and Applied Logic Volume 169, Issue 12, December 2018, pp. 1317-1334.
  61. (with G. Fernandes) Tall cardinals in extender models, accepted for publication in the Notre Dame J. Formal Logic on Feb 25, 2021, pdf.
  62. (with N. Barton, A. Caicedo, G. Fuchs, J. Hamkins, and J. Reitz) Inner-model reflection principles, pdf, Studia Logica 108 (2020), pp. 573-595.
  63. (with F. Castiblanco) When is a given real generic over L? pdf, MLQ, accepted for publication on June 25, 2021.
  64. (with V. Kanovei) Definable Hamel bases and ACω(R), Fund. Math. 253 No. 3 (2021), pp.239-256
  65. From set theoretic to inner model theoretic geology, to appear in "Research Trends in Contemporary Logic," edited by A. Daghighi.
  66. (with D. Asperó) Martin's Maximum++ implies Woodin's Axiom (*) (final version as of March 18, 2021), Annals of Mathematics 193 (3) (2021), pp. 793-835.
  67. (with M. Beriashvili) Mazurkiewicz sets in the Cohen-Halpern-Levy model, Georgian Mathematical Journal 29 no. 3 (2022), pp.343-345
  68. (with S. Hoffelner, P. Larson, and L. Wu) Forcing axioms and definability of NSω1, accepted for publication in the Journal of Symb. Logic.
  69. (with T. Yasuda) Martin’s Maximum*,++c in Pmax extensions of strong models of determinacy, submitted to the Journal of Symb. Logic.


Survey/historical papers:

  1. Wozu brauchen wir grosse Kardinalzahlen? Mathematische Semesterberichte 53 (2006), pp. 65 - 80. PS, PDF
  2. Kurt Gödel (1906-1878), DMV-Nachrichten 14 (2006), pp. 42 - 45; English translation: Newsletter of the European Math. Society 62 (2006), pp. 29 - 31; Chinese translation: Mathematical Advance in Translation, vol. no. 4 (2010), pp. 338--342.
  3. (with D. Asperó) Wieviele reelle Zahlen gibt es?, Mathematische Semesterberichte 70 (2023), pp. 1–-15.

Manuscript written by Ronald Jensen on fine structure, inner model theory, and the core model below one Woodin cardinal

·  (typed by Martina Pfeifer, Fabiana Castiblanco, Shervin Sorouri, and Taichi Yasuda, sponsored by anonymous donors): version as of March 19, 2024. Individual sections of this manuscript my be downloaded at the bottom of this page.

Notes and preprints

  1. Handwritten script on the L hierarchy and the Jensen covering lemma (in German): Kap. 1, Kap. 2, Kap. 3, Kap. 4, Kap. 5, Kap. 6.
  2. The Delfino problem # 12, handwritten, 50 pages. (Talk at Bonn.) PDF. Link to Philipp Doebler's writeup of Steel's solution to the 12th Delfino Problem: PDF.
  3. Link to Benjamin Claverie's writeup of the Dodd--Jensen Covering Lemma below 0-dagger: PDF.
  4. (joint with J. Steel) The strength of AD (contains an outline of Woodin's core model induction, new version as of 07/04/06), preprint. PS, PDF.
  5. A note on an alleged proof of the relative consistency of P=NP with PA, preprint. PS, PDF. Cf. also here and there.
  6. A simple proof of \Sigma^1_3 correctness of K, preprint. DVI, PDF.
  7. Sharps and the \Sigma^1_3 correctness of K, preprint.DVI, PDF.
  8. From Wadge comparability to determinacy, preprint. PDF.
  9. ACA_0, Pi^1_1-CA_0, and the semantics of arithmetic, and BG, BG + Sigma^1_1-Ind, and the semantics of set theory, 10/17/02, note. PS, PDF.
  10. (with P. Schlicht) ZFC without parameters, PDF.
  11. Projective sets and large cardinals, handwritten, 28 pages. (Talk at Kiel.) PDF.
  12. On NS being saturated, new version as of Nov 13, 2021.
  13. Link to Sandra Uhlenbrock's writeup of an account of Woodin's HOD conjecture (in German): PDF.
  14. (with B. Claverie) Ideal extenders, PDF.
  15. (with G. Fuchs, E. Schimmerling, F. Schlutzenberg, S. Uhlenbrock, T. Wilson) A weak (?) consequence of determinacy, PDF.
  16. (with Mariam Beriashvili) Bernstein sets don't give Vitali sets , Luzin and Sierpiński sets in N, and Realizing [...] as a symmetric model. PDF: Some pathological sets in a special model of set theory.
  17. (with Mariam Beriashvili) Bernstein set with a large continuum but no axiom of choice.
  18. A ZFC-example of a forcing which is semi-proper but not proper. The citation [Cox] refers to a posting by Sean Cox.
  19. A note on the reals of C*
  20. (with Grigor Sargsyan and Farmer Schlutzenberg) Varsovian models, II (1st part), Varsovian models, II (2nd part), Varsovian models, II (3rd part), Varsovian models, II (4th part), Varsovian models, II (5th part), Varsovian models, II (6th part), Varsovian models, II (appendix), Varsovian models, II (appendix 2) .
  21. (with Grigor Sargsyan) The number of Woodin cardinals in a core model.
  22. Bukowský and Varsovian models, Vopěnka and Balcar on generic extensions.
  23. The triangular embedding theorem for L(R).
  24. A game theoretic characterization of remarkable cardinals.
  25. (with L. Wu and L. Yu) Hamel bases and the principle of dependent choice, preprint, PDF.
  26. Mazurkiewicz sets in the Cohen-Halpern-Levy model.
  27. A model with everything except for a well-ordering of the reals.
  28. Groszek and Slaman on Prikry's problem.
  29. (with Paul Larson and Liuzhen Wu) NSω1 is not Π1 definable, Addendum to "NSω1 is not Π1 definable".
  30. Sacks forcing preserves selective ultrafilters.
  31. A note on the < κ mantle.
  32. GCH and ⋄ in L[U].
  33. On a question of Xianghui Shi.
  34. A remark on a theorem by Chan-Jackson-Trang.
  35. HODL(R), Vopěnka, and Woodin's extender algebra.
  36. MAω1 implies NSω1 is not ω1-dense (A. Taylor).
  37. The extender algebra for mice without Woodin cardinals, remarks on a paper by S. Friedman.
  38. Notes from my Pmax course in 2021-22 which were produced by Azul Fatalini are available here.
  39. (with D. Asperó) Martin's Maximum is Π2complete.
  40. -CH and (*).

Open problem lists

  1. LIST OF OPEN PROBLEMS IN INNER MODEL THEORY, edited jointly with John Steel.
  2. Links to a list of problems that was produced at the AIM meeting "Recent advances in core model theory," organized by E. Schimmerling and J. Steel in Dec 13-17, 2004: PDF, PDF.
  3. List of problems that was produced by Per Stinchcombe at the AIM meeting "Descriptive inner model theory," organized by R. Schindler and J. Steel in June 02-06, 2014: PDF.
  4. List of problems that was produced at the 1st Girona meeting on inner model theory, organized by R. Schindler, J. Steel, and J. Vergés in July, 2018: PDF.
  5. List of problems that was produced at the Berkeley conference on inner model theory, organized by R. Schindler and J. Steel in July, 2019: PDF.

Skripten zu Vorlesungen und Seminaren

  1. Lecture course on iterated forcing, notes taken by T. Yasuda: week 1, week 2, week 3, week 4, week 5.
  2. Skript zur Vorlesung "Logik 1", Version vom 03.04.2020: PDF-Datei. (Tipp-)Fehler bitte an rds at math dot uni-muenster dot de.
  3. Die auf dem Hochschultag am 13.11.2014 verteilten Logikrätsel als PDF-Datei.
  4. Mein Hochschultagsvortrag vom 19.11.2020 über Hilberts Hotel und die Mathematische Logik auf youtube.
  5. Exercise sheets that came with my set theory course in 2020-21: no. 1, no. 2, no. 3, no. 4, no. 5, no. 6, no. 7, no. 8, no. 9, no. 10.

Service activities

  1. Former co-editor of the Journal of Symbolic Logic (2008-2012).
  2. Editor-in-chief of the Archive for Mathematical Logic (2009-present).
  3. Co-editor of the Ontos Verlag series in Mathematical Logic (2013-present). Information for potential authors may be downloaded here.
  4. Co-editor of the Mathematische Semesterberichte.
  5. Secretary/Vice president of the European Set Theory Society (2015-present).
  6. Former editor of the Münster Journal of Mathematics.
  7. Former treasurer of the IUHPS/DLMPS (International Union of the History and Philosophy of Science/Division of Logic, Methodology, and Philosophy of Science) (2008-2012)
  8. One of the former chairmen of the DVMLG, the German Logic Society (2008-2011).
  9. Organizer of our department's activity at the annual open house event, the Hochschultag Münster, 2006-present.
  10. Member of the Mathematics Panel of the Czech Science Foundation, Apr 01, 2019-March 31, 2021. See here.
  11. Vertrauensdozent der Studienstiftung des deutschen Volkes. Fotos von einem Treffen mit meiner Stipendiatengruppe, 2006. 2007. 2008. Stockholm, 2009. Eiskeller Altenberge, 2017.
  12. Co-organizer (with R. Jensen and M. Magidor) of a mini-workshop in inner model theory, Apr 30 - May 06, 2006, Oberwolfach.
  13. Co-organizer of the Logic Colloquium, July 27 - Aug 2, 2006, Nijmegen.
  14. Co-organizer (with E.Schimmerling) of a mini-symposium in set theory during the DMV meeting, Bonn, Sept 18-22, 06.
  15. Organizer of the PohlersFest, July 17-19, 2008, Münster. Pictures!
  16. Co-organizer of the 2nd European Set Theory Conference (Bedlewo, Poland), July 6-10, 2009.
  17. Co-organizer (with R. Jensen and M. Magidor) of a mini-workshop in inner model theory, Nov 08 - 14, 2009, Oberwolfach.
  18. Co-organizer (with J. Steel) of the 1st conference on the core model induction and hod mice in Münster, July 19 -- Aug 06, 2010.
  19. Co-organizer of the Colloquium Logicum, Münster, Sept 22-24, 2010.
  20. Co-organizer (with J. Steel) of the 2nd conference on the core model induction and hod mice in Münster, Aug 08 -- Aug 19, 2011.
  21. Seminar im Rahmen der Sommerakademie der Studienstiftung in Neubeuern 2013
  22. Co-organizer, with J. Steel, of the Descriptive inner model theory meeting at the American Institute of Mathematics, Palo Alto, June 02-06, 2014.
  23. Co-organizer, with J. Steel, of the Mitchell fest, Berkeley, June 07-08, 2014.
  24. Co-organizer, with J. Steel, of the Descriptive inner model theory meeting, Berkeley, June 09-13, 2014.
  25. Co-organizer of the 5th European Set Theory Conference (Cambridge, England), Aug 24-28, 2015.
  26. Co-organizer (with J. Steel) of the 3rd Münster conference on inner model theory, the core model induction, and hod mice, July 20 -- 31, 2015.
  27. Co-organizer of the Logic Colloquium 2016, Leeds.
  28. Co-organizer (with M. Magidor and J. Väänänen) of an Intensive Research Program on "Large Cardinals and Strong Logics", CRM, Bellaterra (Catalunya), Sept 05--Dec 16, 2016.
  29. Co-organizer (with I. Farah, S. Friedman, and W.H. Woodin) of a workshop in set theory, Oberwolfach, Feb 12--18, 2017.
  30. Co-organizer (with J. Steel) of the 4th Münster conference on inner model theory, July 17 -- Aug 01, 2017.
  31. Co-organizer (with M. Magidor, J. Steel, and W.H. Woodin) of a set theory conference, WWU Münster, Aug 02--Aug 04, 2017.
  32. Co-organizer (with J. Steel and J. Vergés) of the 1st Girona conference on inner model theory, July, 2018.
  33. Member of the scientific committee of the Third International Conference "Modern Problems in Applied Mathematics," Tbilisi , Sept, 2018.
  34. Co-organizer (with J. Steel) of the Berkeley conference on inner model theory, July, 2019.
  35. Co-organizer (with I. Farah, D. Sinapova, and W.H. Woodin) of a workshop in set theory, Oberwolfach, Apr 05--11, 2020. Cancelled due to COVID-19.
  36. Co-organizer (with F. Schlutzenberg and J. Steel) of the Münster conference on inner model theory, June 15-26, 2020. Cancelled due to COVID-19.
  37. Co-organizer (with F. Schlutzenberg and J. Steel) of the Münster conference on inner model theory, June 28-July 09, 2021. Cancelled due to COVID-19.
  38. Co-organizer (with I. Farah, D. Sinapova, and W.H. Woodin) of a workshop in set theory, Oberwolfach, Jan 09 -- 15, 2022.
  39. Co-organizer (with F. Schlutzenberg and J. Steel) of the Münster conference on inner model theory, June 20-July 01, 2022.
  40. Co-organizer (with James Cummings, Noam Greenberg, Liang Yu, and Yang Yue) of a workshop at the IMS, Singapore, June 12-July 07, 2023.
  41. Co-organizer (with Sandra Müller and John Steel) of an inner model theory workshop, Vianna, 2024.
  42. Co-organizer (with Vera Fischer, Menachem Magidor, Christian Rosendal, Dima Sinapova [chair], and Philip Welch) of the 9th European Set Theory Conference, Münster, 2024.
  43. Co-organizer (with Ilijas Farah, Dima Sinapova, and W. Hugh Woodin) of a set theory workshop at Oberwolfach, Jan 12-17, 2025.

Undergrad students

  1. Diploma theses: Benjamin Claverie (2005), Philipp Doebler (2006), Thilo Weinert (2008), Philipp Lücke (2008), Dominik Adolf (2008), Marek Wyszkowski (2009), Carsten Szardenings (2010), Jakob Rittberg (2010), Max Giersberg (2010), Tobias Förster (2012), Max Temme (--), Barzin Hadjimoradi (2015).
  2. Bachelor's theses: Sandra Uhlenbrock (2010), Jan Wulf (2010), Merle Erpenbeck (2011), Sabine Schneider (2011), Christof Beierle (2012), Eike Bunn (2012), Momme Steffen (2012), Marvin Landwehr (2012), Jonas Fox (2013), Stefan Miedzianowski (2013), Maximilian Gievert (2013), Patrick Aguilar (2018), Benjamin Reuting (2014), Kolja Hartmann (2015), Lennart Holtkötter (--), Martin Stückemann (2016), Franziska Popp (2016), Robin Puchalla (2016), Robin Graeber (2016), Claudia Giesen (2016), Simon Dröge (2016), Sebastian Greve (2016), Kira Sielenkämper (2019), Necip-Soner Bölükbas (--), Philipp Kretschmer (2021), Doreen Töns (2021), Mirko Bartsch (2022), Thea Schäfer (2022), Aron Rupperath (2022, 2nd referee), Mathis Brüggemann (2023), Leon Glünsing (2024).
  3. Master's theses: Sandra Uhlenbrock (2012), Eike Bunn (2016), Momme Steffen (2014), Marvin Landwehr (2016), Stefan Miedzianowski (2016), Jonas Fox (2018), Robin Graeber (2019), Robin Puchalla (2020), Markus Poehler (2019), Claudia Giesen (2020), Manuel Fiedler (2021), Jan Kruschweski (2021), Kira Sielenkämper (2021), Karl Westphal (2023), Shervin Sorouri (2023), Taichi Yasuda (2024).

Ph.D. students

  1. Dr. Dominik Adolf (finished in 2013), until recently PostDoc at the Department of Mathematics, Bar-Ilan University, Ramat-Gan (Israel)
  2. Dr. Daniel Busche (DFG project no. SCHI 484/2-2, "Anwendungen der Theorie der Kernmodelle in der Kardinalzahlarithmetik (bzw. pcf-Theorie)", finished in 2007)
  3. Dr. Benjamin Claverie (DFG project no. SCHI 484/3-1, "Anwendungen der Theorie der inneren Modelle auf Fragen der Absolutheit und Korrektheit", finished in 2010)
  4. Dr. Fabiana Castiblanco, finished in 2018
  5. Prof. Dr. Philipp Doebler (DFG project no. SCHI 484/3-1, "Anwendungen der Theorie der inneren Modelle auf Fragen der Absolutheit und Korrektheit", finished in 2010). Now professor in Dortmund.
  6. Azul Fatalini, started Nov 01, 2020.
  7. Prof. Dr. Daisuke Ikegami (University of Amsterdam, finished in 2010), now at Institute of Logic and Cognition, Department of Philosophy, Sun Yat-sen University, Guangzhou (China).
  8. Dr. Marios Koulakis (MALOA project), finished in 2015, now Data Scientist and Engineer at Nulogy, TranQuant Inc., ASD, Toronto (Canada)
  9. Dr. Andreas Lietz (finished in 2023, winner of the Sacks Prize for the most outstanding dissertation in mathematical logic), now PostDoc at TU Wien (Austria)
  10. Dr. Philipp Lücke (DFG project no. SCHI 484/4-1, "The interplay between algebra and logic", SFB 878, finished in 2012), now PostDoc at the University of Hamburg.
  11. Stefan Miedzianowski (DFG-Projekt SCHI 484/8-1, "Die Geologie Innerer Modelle").
  12. Dr. Philipp Schlicht ("Thin equivalence relations in L(R) and inner models", finished in 2008), now PostDoc at the University of Auckland (New Zealand)
  13. Shervin Sorouri, started Oct 01, 2023.
  14. Xiuyuan Sun, started Oct 01, 2020.
  15. Prof. Dr. Sandra Müller (nee Uhlenbrock), finished in 2016, now Professor at the University of Vienna (Austria)
  16. Taichi Yasuda, started March 01, 2024.
  17. Prof. Dr. Gabriel Zanetti Nunes Fernandes, finished in 2018, now Professor at the Department of Mathematics, University of Sao Paolo (Brazil)

PostDocs

  1. Dr. Ben De Bondt (started 2024)
  2. Prof. Dr. Yong Cheng (2014-15), went to Wuhan University (China)
  3. Prof. Dr. Sean Cox (2009-12), went to VCU (USA)
  4. Prof. Dr. Gunter Fuchs (2004-09), went to CUNY (USA)
  5. Prof. Dr. Daniel Herden (2009-10)
  6. Dr. Stefan Hoffelner (2018-24)
  7. Dr. Hossein Lamei Ramandi
  8. Dr. Rene Schipperus (W2 position replacement, 2009-10). Series on linear algebra: History and introduction to linear equations
  9. Dr. Philipp Schlicht (W2 position replacement, 2015-16)
  10. Dr. Farmer Schlutzenberg (Junior professor, 2017-23), went to Vienna (Austria)
  11. Prof. Dr. David Schrittesser (2013), now professor at Harbin (China)
  12. Dr. Yizheng Zhu (2012-17), went to the School of Mathematical Sciences, Chinese Academy of Sciences

Invited talks

  1. Oxford, 05/26/94, Bicephali below o(k)=k++.
  2. Berlin, Dec. 95, Combinatorial applications of the core model.
  3. Fine structure meeting at Oberwolfach, July 97, Iterability below a measurable limit of strongs.
  4. Non-meeting at Irvine, Dec 97, Regularity properties of sets of reals.
  5. VIG at UCLA, Jan. 98, Strong cardinals and sets of reals in L_{omega_1}(R).
  6. L.A. Logic Colloquium, Oct. 98, Nice sets of reals and choice-like principles.
  7. Berkeley Logic Colloquium, Dec. 98, Coding into mice and other subtleties.
  8. ASL Annual Meeting at San Diego, March 99, Coding into L(R), cancelled.
  9. Lecture series at Bonn, April 99, The Delfino problem # 12.
  10. Greater Boston Logic Meeting at MIT, May 99, Projective sets and singletons.
  11. Berlin Logic Colloquium, Dec. 99, Generic absoluteness.
  12. Set theory meeting at Oberwolfach, Dec. 99, The core model for almost linear iterations. Picture.
  13. ASL Annual Meeting at Urbana-Champaign, June 2000, Inner models and 0^hand-grenade.
  14. 6eme Atelier Int'l de Theorie des Ensembles at Luminy, 09/20/00, Proper forcing and remarkable cardinals.
  15. Berlin Logic Colloquium 01/15/01, Das Kernmodell für fast lineare Iterationen.
  16. München 01/17/01, Projektive Mengen und Kernmodelle.
  17. Non-meeting at Bonn, 01/19/01, Core models.
  18. Münster 02/09/01, Projektive Mengen reeller Zahlen und Kernmodelle. DVI.
  19. Fine structure meeting at Oberwolfach, Hand grenades I + II, 02/26 + 02/28/01
  20. Fine structure meeting at Oberwolfach, A universal weasel, 03/01/01.
  21. ASL European Summer meeting, Vienna, 08/10/01, Mutual stationarity in L[E].
  22. Set theory workshop, Vienna, 08/13/01: Iterates of the core model.
  23. Foundations of the formal sciences III, Vienna, 09/23/01, Projective sets of reals and core models. DVI.
  24. Set theory meeting, Oberwolfach, 01/21/02: Mutual stationarity in L[E].
  25. Paris 06/17/02: Cardinal arithmetic and determinacy.
  26. Bonn 06/20/02: Einfache Korrektheitsbeweise. DVI.
  27. München 06/24/02: Kardinalzahlarithmetik und Determiniertheit.
  28. ASL European Summer meeting, Münster, 08/05/02: Transfer theorems. Slides: PS, PDF.
  29. 7th Atelier Int'l de Theorie des Ensembles at Luminy, 09/19/02, Pcf theory and Woodin cardinals.
  30. Kiel, Dec 11, 02, Projektive Mengen und grosse Kardinalzahlen, seminar talk.
  31. Kiel, Dec 13, 02, Projektive Mengen reeller Zahlen, Colloquium talk.
  32. Fine structure meeting, Bonn, July 07-11, 03, Forcing axioms and the constructible universe.
  33. Barcelona conference on set theory, Sept 16-20, 03, 4-hour course. The role of absoluteness and correctness. Slides in dvi.
  34. Bonn, Nov 20, 03, Verallgemeinerungen von Martins Axiom.
  35. Barcelona, Feb 17, 04, Semi-proper forcing and remarkable cardinals.
  36. Antrittsvorlesung, Jun 16, 04, Wozu bauchen wir grosse Kardinalzahlen? ps-file.
  37. DVMLG meeting, Heidelberg, Sept 17, 04, Cardinal arithmetic and determinacy ps-file.
  38. Eighth Luminy Set Theory Workshop September 20 - 24th, 2004, BMM - one answer and one problem.
  39. DMV meeting, Mainz, June 05, Projective equivalence relations and inner model theory.
  40. TU Darmstadt, July 06, 05, Wozu brauchen wir grosse Kardinalzahlen?
  41. Freiburg, Dec 02, 05, Äquivalenzrelationen und grosse Kardinalzahlen. ps-file. pdf-file.
  42. Fine structure workshop, Oberwolfach, May 06, The self-iterability of L[E].
  43. British Logic Colloquium, Oxford, Sept 06, Pcf theory and determinacy.
  44. Colloquium Logicum, Bonn, Sept 06, If every uncountable cardinal is singular, then AD holds in L(R).
  45. Ninth Luminy Set Theory Workshop, Oct 3, 06, Diamond^+_kappa,lambda in L[E]
  46. Bonn Nov 30, 06, The strength of PFA.
  47. Hausdorff Center for Math, Bonn, Jan 23, 07, The P vs. NP problem for infinite time Turing machines
  48. Logic Colloquium, UC Berkeley, Sept 21, 07, Forcing axioms and large cardinals
  49. UC Irvine, Nov 05, 07, BMM, canonical functions, and precipitous ideals
  50. UC Irvine, Nov 26, 07, Proving projective determinacy, ps-file, pdf-file.
  51. Tenth Luminy workshop in Set Theory, Sept 08, Π_2 consequences of BMM plus NS is precipitous.
  52. Paris 7, Oct 08, Π_2 consequences of BMM plus NS is precipitous.
  53. Bonn June 12, 09, Mining strength from hypotheses incompatible with choice
  54. Workshop on large cardinals, Wien, June 09, Bounded forcing axioms and reflection
  55. ASL European Summer meeting, Sophia (Bulgaria), July 31 to August 5, 2009, three-hour tutorial course on "the evolution of inner models": part 1, part 2, part 3.
  56. Mittag-Leffler Institute, Djursholm, Sweden, Woodin's axiom (*), bounded forcing axioms, and related issues, part 1 and 2, Oct 01 and 29, 2009.
  57. Young set theorist's workshop, Raach am Hochgebirge, tutorial course on inner model theory, Feb 15--19, 2010.
  58. Graduate center, New York City, March 26, 2010, Π_2 consequences of BMM plus NS is precipitous
  59. Fields Institute, Toronto, April 09, 2010, Π_2 consequences of BMM plus NS is precipitous.
  60. Math colloquium, München, April 23, 2010, Sind große Kardinalzahlen entbehrlich?, PDF.
  61. Barcelona, April 29, 2010, Forcing axioms and determinacy
  62. Amsterdam, June 01, 2010, Mice and set theoretic geology
  63. München, Nov 03, 2010, Forcing-Axiome und die Feinanalyse von Hω2, pdf.
  64. Harvard, "The Higher Infinite: 50 Years of Large Cardinals and Inner Models", Feb 18--20, 2011, Generic Iterations and Forcing Axioms
  65. Bonn, April 18, 2011, Resectionable truth
  66. UC Irvine, May 04, 2011, Resectionable and other Σ1 truths
  67. LPS, UC Irvine, May 06, 2011, Dilemmas and truths in set theory, PDF.
  68. Edinburgh, July 2011, BMM*
  69. Palermo, April 03 and 04, 2012, Recent insights concerning the continuum problem and A dilemma in the philosophy of set theory, PDF1 and PDF2
  70. Barcelona, June 2012, A proof of Jensen's Covering Lemma, lecture series.
  71. Luminy, Sept 2012, Tutorial on Jensen's L-forcing, 1st lecture, 2nd lecture, 3rd lecture.
  72. Oxford, Oct 08 , 2012, Dilemmas and truths in set theory.
  73. Fields Institute, Toronto, Nov 12, 2012, An Axiom.
  74. Barcelona, Dec 15, 2012, Martin's Maximum with an asterisk.
  75. UC Irvine, Feb 25, 2013, Stationary reflection, mouse reflection, and strategy reflection.
  76. Tecklenburg, May 02, 2013, Wozu brauchen wir große Kardinalzahlen?
  77. Wien, Sept 25, 2013, Does analytic determinacy yield zero-sharp?
  78. Bonn, Oct 21, 2013, Does analytic determinacy yield zero-sharp?
  79. UC Irvine, Feb 24, 2014, Harrington's Principle and remarkable cardinals.
  80. Harvard University, March 26, 2014, Martin's Maximum with an asterisk.
  81. Bonn, May 24, 2014, Martin's Maximum with an asterisk.
  82. Bristol, July 06, 2014, TBA, cancelled.
  83. Poznan, Sept, 2014, cancelled.
  84. Hebrew University, Jerusalem, Feb 27, 2015, Martin's Maximum, Woodin's (*), or both?
  85. CUNY, March 30, 2015, Harrington's Principle and remarkable cardinals.
  86. MAMLS meeting, CMU, May 30-31, 2015, Singular cardinals, pcf theory, and determinacy.
  87. Logic Colloquium 2015, Helsinki, August 03-08, 2015, Martin's Maximum, Woodin's (*), or both?. There is a video of this talk!
  88. Conference on set theory and model theory, Tehran, Iran, Oct 12-16, 2015, Remarkable cardinals. Some notes: Part 1, Part 2.
  89. Bonn, Dec 04, 2015, PFA-.
  90. Tel Aviv University, Feb 16, 2016, PFA-.
  91. Hebrew University, Jerusalem, Feb 19, 2016, Varsovian models. This talk can be watched on youtube.
  92. Rutgers University, March, 2016, L-forcing and local consequences of MM and (*) (lecture series)
  93. CUNY, March 18, 2016, PFA-.
  94. Münster model theory month, May 02, 2016, The continuum hypothesis, MM, and (*).
  95. 1st IRVINE CONFERENCE on DESCRIPTIVE INNER MODEL THEORY and HOD MICE, July, 2016, Varsovian models.
  96. Universitat de Barcelona, Oct 14, 2016, More fake cardinals.
  97. Workshop, Tbilisi (Georgia), Oct, 2016, Bernstein sets don't give Vitali sets.
  98. Workshop on the Applications of strong logics in other areas of mathematics, CRM, Bellaterra (Catalunya), Nov, 2016, Martin's Maximum with an asterisk.
  99. Bonn Jan 09, 2017, A Hamel basis for the reals without choice.
  100. Beijing March 10, 2017, Martin's Maximum, Woodin's (*), or both?, Colloquium talk.
  101. Beijing March 14, 2017, Varsovian models.
  102. Luminy, Oct, 2017, Varsovian models with more Woodin cardinals.
  103. Barcelona, Oct 30, 2017, Hamel bases without the axiom of choice.
  104. University of Warsaw, March 14, 2018, "Paradoxical" sets with no well-ordering of the reals.
  105. Chinese Mathematical Logic Conference, Qiannan Normal University for Nationalities, Duyun, Guizhou, P. R. China, May 12-13, 2018, "Paradoxical" sets with no well-ordering of the reals.
  106. Beijing Normal University, May 18, 2018, Remarkable and other fake cardinals.
  107. May 22, 2018, Institute of Mathematics, Chinese Academy of Sciences, Beijing, Ground generation.
  108. Steklov Institute, Moscow, Oct 15 + 22, 2018, "Paradoxical" sets with no well-ordering of the reals. These talks can be watched online: part 1 and part 2.
  109. Conference on "Reflections on Set Theoretic Reflection," Nov 2018, Montseny, Catalonia, Burstin bases and well-ordering the reals. PDF
  110. IPM, Tehran, Iran, Feb 23 - 28, 2019, lecture course on "The extender algebra and its variants", see here.
  111. Bar-Ilan University, Ramat-Gan, Israel, March 25, 2019, Variants of the extender algebra and their applications
  112. Hebrew University, Jerusalem, Israel, March 27, 2019, "Paradoxical" sets with no well-ordering of the reals
  113. Institute of Mathematics, Czech Academy of Sciences, Apr 16, 2019, "Paradoxical" sets with no well-ordering of the reals
  114. Institute of Mathematics, Czech Academy of Sciences, Apr 17, 2019, Variants of the extender algebra and their applications
  115. Institute for Mathematical Sciences, Singapore, June 2019, MM++ implies (*). You may watch this talk on youtube.
  116. Set theory workshop, Luminy, Sept 2019, A proof of a version of the Ω conjecture plus an application.
  117. IPM Tehran, Iran, Oct 2019, MM++ implies (*).
  118. Bonn, Nov 08, 2019, MM++ implies (*).
  119. RIMS set theory workshop, Kyoto, Nov 2019, MM++ implies (*).
  120. Jerusalem, March 04, 2020, Forcing Woodin's axiom (*) over a model of ZFC.
  121. Wuhan University, May 2020, t.b.a.. Cancelled due to COVID-19.
  122. Logic Workshop in Nanjing, May 2020, t.b.a.. Cancelled due to COVID-19.
  123. Set theory workshop in Vienna, July 2020, t.b.a.. Cancelled due to COVID-19.
  124. 5 day lecture series, Fudan University, Shanghai, China, August 17-21, 2020, Forcing axioms and the axiom (*), via zoom.
  125. UI Chicago, Sept 15, 2020, Martin's Maximum++ implies the Pmax axiom (*), via zoom.
  126. CUNY Grad Center, Sept 25, 2020, Martin's Maximum++ implies the Pmax axiom (*), via zoom. Recordings of my talk and the follow-up talk by David Asperó.
  127. University of Helsinki, Nov 04, 2020, Martin's Maximum++ implies the Pmax axiom (*), via zoom.
  128. Fields Institute, Toronto, Nov 13, 2020, Martin's Maximum++ implies the Pmax axiom (*), via zoom.
  129. Wuhan University, Dec 08, 2020, How many real numbers are there?, via zoom.
  130. Torino/Udine, Jan 22, 2021, Martin's Maximum++ implies the Pmax axiom (*), via zoom. Here is a recording of this talk.
  131. IPM, Tehran, Iran, Feb 03, 2021, A definable Hamel basis without choice, via zoom. Here is a recording of this talk.
  132. Logic Colloquium, Harvard University, Feb 11, 2021, (*) is a bounded forcing axiom, via zoom.
  133. Set theory conference, Luminy, Sept 13, 2021, Mazurkiewicz sets.
  134. Oxford, Oct 28, 2021, Martin's Maximum++ implies the Pmax axiom (*)
  135. Münster C*-algebras seminar, Set theory and the continuum hypothesis, Jan 18, 2022.
  136. IMU + DMV meeting, Beer Sheva, Feb 2022, plenary talk. Cancelled due to COVID-19.
  137. IMPAN, Gdansk, seminar talk, Feb 09, 2022.
  138. IMPAN, Gdansk, colloquium talk, Set theory and the continuum hypothesis, Feb 10, 2022.
  139. UC Irvine, colloquium talk, Set theory and the continuum hypothesis, Apr 21, 2022.
  140. IMS Logic Summer School 2022 speaker, July 04-08, 2022.
  141. Set theory conference, Hebrew University of Jerusalem, July 10-14, 2022
  142. Hausdorff lecture, Turin, Aug 29, 2022. Slides.
  143. Waseda University, Tokio, Martin's Maximum is Π2 complete, Oct 06, 2022.
  144. Colloquium talk, TU Vienna, Dec 15, 2022, Martin's Maximum, Woodin's Pmax axiom (*), and Cantor's Continuum Problem.
  145. TU Vienna, Dec 16, 2022, Martin's Maximum is Π2 complete.
  146. Conference of the Iranian Association for Logic, Feb 23, 2022, Martin’s Maximum, Woodin's Pmax axiom (*), and Cantor’s Continuum Problem.
  147. ASL meeting, Irvine, CA, March 2023, Martin's Maximum, Woodin's (*), and beyond.
  148. Logic Colloquium, Berkeley, CA, April 2023, Martin's Maximum and Woodin's (*).
  149. 1st Int'l Conference on Basis Sciences, Beijing (China), July 2023, Martin's Maximum and Woodin's (*).
  150. Luminy (France), September 2023, BMM*,++c
  151. Baltic Set Theory Seminar, Gdansk (Poland), Nov 2, 3, 6, 2023, The *-version of Martin's Maximum.
  152. BLAST, Denton, TX, March 2024, Martin's Maximum with an asterisk, revisited.
  153. plenary speaker, European Congress of Mathematics, Sevilla (Spain), March 2023, t.b.a.
  154. pleanary speaker, 2nd Int'l Conference on Basis Sciences, Beijing (China), July 2024, t.b.a.
  155. Munich, Oct 31, 2024, t.b.a.

Contributed talks

  1. ASL European Summer Meeting at Haifa, Aug. 95, On a Chang conjecture.
  2. BEST at Boise, March 97, On (the consistency strenth of) certain consequences of AD.
  3. ASL European Summer Meeting at Leeds, July 97, On patterns of cardinals with the tree property.
  4. Berlin, 06/25/01, Habilitationskolloquium, P = NP? ps-file , pdf-file
  5. Münster, July 27--30, 2010, Tutorial on the core model induction.
  6. Zentrum für Wissenschaftstheorie, Münster, 22.06.11, Braucht die Mathematik neue Axiome? PDF
  7. Münster, Aug 2011, BPFA plus a precipitous ideal on ω1

Reviews

See also here

  1. Besprechung von Sets and Proofs (Cooper, Truss, eds.) für die Int'l Math. News 185.
  2. Review of Cardinal Arithmetic by M. Holz, K. Steffens, and E. Weitz for Studia Logica.
  3. Besprechung von Fine structure and class forcing von S.D. Friedman für die Int'l Math. News 188.
  4. Besprechung von On numbers and games von J. Conway für die Int'l Math. News 189.
  5. Besprechung von From Trotzy to Gödel. The life of Jean van Heijenoort von A.B. Feferman für die Int'l Math. News 189. PDF.
  6. Review of Consequences of an exotic definition for P=NP by N.C.A.da Costa and F.A.Doria. PS.
  7. Review of Die Logik der Unbestimmtheiten und Paradoxien by Ulrich Blau for the BSL. PDF.
  8. Review of Combinatorial Set Theory by L.J. Halbeisen for the Jahresberichte der Deutschen Math.-Vereinigung. PDF.
  9. Review of Forcing over models of determinacy by Paul Larson. PDF.

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