IN MICE WE TRUST

© Gregor Schindler 2016

4th Münster conference on

inner model theory

Institut für Mathematische Logik, WWU Münster,

July 17 -- Aug 01, 2017

Organizers: Ralf Schindler (Münster), John Steel (Berkeley)


This conference will be a sequel to the 1st Conference on the core model induction and hod mice that was held in Münster (FRB), July 19 -- August 06, 2010, to the 2nd Conference on the core model induction and hod mice that was held in Münster (FRG), August 08 -- 19, 2011, to the AIM Workshop on Descriptive Inner Model Theory, held in Palo Alto (CA), June 02 -- 06, 2014, to the Conference on Descriptive Inner Model Theory, held in Berkeley (CA) June 09 -- 13, 2014 to the 3rd Münster Conference on inner model theory, the core model induction, and hod mice that was held in Münster (FRG), July 20 -- 31, 2015, as well as to the 1st Irvine conference on descriptive inner model theory and hod mice that was held in Irvine (CA), July 18 -- 29, 2016.

Once more, this conference will draw together researchers and advanced students with an interest in inner model theory, in order to communicate and further explore this recent work. There will be courses and single talks.

We will meet Monday--Friday, with 2 hours of lecture in the morning and 2 hours of lecture in the early afternoon. This will leave ample time for problem sessions, informal seminars, and other interactions in the late afternoons and evenings.

The conference will take place at the Department of Mathematics and Computer Science, Univ. of Muenster, Seminar room N2 (1st week) and lecture hall M6 (2nd and 3rd week).

The conference organizers gratefully acknowledge financial support from the American NSF (through Grigor Sargsyan and John Steel), from the Marianne and Dr. Horst Kiesow-Stiftung, Frankfurt a.M., and from the German logic society, DVMLG.

Tentative schedule:

Mon, July 17 Tue, July 18 Wed, July 19 Thu, July 20 Fri, July 21
9:30--10:45 Schlutzenberg: Tutorial I part 1 Wilson: Tutorial II part 1Zhu: Tutorial I part 3Zeman: Tutorial III part 2Goldberg 1
11:15--12:30 Schlutzenberg: Tutorial I part 2 Wilson: Tutorial II part 2Zhu: Tutorial I part 4Zeman: Tutorial III part 3 Goldberg 2
14:30--15:45 Zeman: Tutorial III part 1 Ben-Neria 1Wilson: Tutorial II part 3 Schindler 1 Zeman: Tutorial III part 4
16:15--17:30 "Paradoxical sets" seminar: Beriashvili Ben-Neria 2Wilson: Tutorial II part 4 Schindler 2 Ben-Neria 3
17:30--∞ -- Problems and Discussions -- Problems and Discussionsfree

Mon, July 24 Tue, July 25 Wed, July 26 Thu, July 27 Fri, July 28
9:30--10:45 Trang Sargsyan I, 1 Jackson Castiblanco Steel: Tutorial IV part 1
11:15--12:30 Zeman: Tutorial III part 5 Sargsyan I, 2 Zeman: Tutorial III part 6 Miedzianowski Steel: Tutorial IV part 2
14:30--15:45 Adolf 1 Uhlenbrock Zeman: Tutorial III part 7 Aguilera Sargsyan II, 1
16:15--17:30 Adolf 2 Fernandes SteelBlue Sargsyan II, 2
17:30--∞ Problems and Discussions Problems and DiscussionsProblems and DiskussionsProblems and Discussionsfree

Mon, July 31 Tue, Aug 01
9:30--10:45 Steel: Tutorial IV part 3 Schlutzenberg 1
11:15--12:30 Steel: Tutorial IV part 4 Schlutzenberg 2
14:30--15:45 Sargsyan free
16:45--17:30 Wilson: Tutorial II part 5 free
17:30--∞ Problems and Discussions Problems and Discussions

Talks and abstracts:

  1. Dominik Adolf: A derived model satisfying Θ ≥ θω2. Abstract: See title. This is joint work with G. Sargsyan. Notes by rds: Adolf, part 1, Adolf, part 2
  2. Juan Aguilera: Making Δ1 Determined Again. Abstract: We prove some results on games of length ω1 that strengthen provably-Δ1 determinacy. This is joint work with Douglas Blue. Notes by rds: Aguilera,
  3. Omer Ben-Neria: The failure of diamond principle at large cardinals. In pursuit of an understanding of the relations between compactness and approximation principles, we address the following question: To what extent do compactness principles assert the existence of a diamond sequence? It is well known that a cardinal κ which satisfies a sufficiently strong compactness assumption must also carry a diamond sequence. However, other results have shown that certain weak large cardinal assumptions are consistent with the failure of the full diamond principle. We will discuss this gap and describe some known and recent results. Notes by rds: Ben-Neria, part 1, Ben-Neria, part 2, Ben-Neria, part 3.
  4. Doug Blue and Martin Zeman: Tutorial III on ◻κ in mice, long extender mice, and least-branch hod mice. Parts 1, 2, 3, 4, and 5 (Zeman): the Schimmerling-Zeman characterization of square in short extender models. Part 6 (Blue): the difficulties for square in plus-one premice. Notes by Stefan Miedzianowski: Zeman, part 1, Zeman, part 2, Zeman, part 3, Zeman, part 4, Zeman, part 5. Slides: Blue.
  5. Fabiana Castiblanco: The ordinal u2 and a thin Δ13 equivalence relation. Abstract: Under the existence of sharps for reals the second uniform indiscernible can be defined as u2 = sup{ ω1+L[x]: x a real }. Suppose that P is Sacks, Mathias, Silver, Miller or Laver forcing. In this talk we will see that if every real has a sharp then u2V= u2VP and, in fact, P does not add any new equivalence class to the Δ13-thin equivalence relation defined by xEy iff ω1+L[x] = ω1+L[y]. File: Castiblanco,
  6. Gabriel Fernandes: Cardinal arithmetic and Woodin cardinals. Abstract: If ω3 < cf (κ) < κ, for all α < κ we have ℶα(α) ∈ κ and S = {α < κ | 2α > α+ } is stationary and co stainary, then there is a mouse M such that M∩OR = κ and M |= ∀α∃δ > α(δ is a Woodin cardinal). This is joint work with Ralf Schindler. Notes by rds: Fernandes
  7. Gabriel Goldberg: Supercompact cardinals and the Mitchell order. Abstract: We introduce a general comparison principle for ultrafilters, the Ultrapower Axiom, that along with GCH implies that the Mitchell order is linear on supercompactness measures. For example, the result applies to the Woodin and Neeman-Steel models at the finite levels of supercompactness, even though in these models many supercompactness measures, and even normal measures, do not appear on the sequence. Notes by rds: Goldberg, part 1, Goldberg, part 2. Notes by Stefan Miedzianowski: Goldberg, part 3.
  8. Steve Jackson: Some new partition and non-partition results from AD. Abstract: Assuming AD, we identify the exact exponent partition properties the successor and double successor of regular limit Suslin cardinals have, and some related questions. This is joint work with Apter, Blass, and Lowe. File: Jackson.
  9. Stefan Miedzianowski: Inner Model Theoretic Geology. Abstract: We analyze the mantle of the least inner model with a strong cardinal which itself is a limit of Woodin cardinals. This is joint work with Ralf Schindler. Notes by rds: Miedzianowski.
  10. Grigor Sargsyan I: PFA implies a model of LSA. Abstract: Exactly what is in the title. Joint work with Nam Trang. Notes by rds: Sargsyan, part 1, Sargsyan, part 2
  11. Grigor Sargsyan II: Strategy Representation Hypotheses below non-domestic hod mice. Abstract: We show that under AD+ if there is non-domestic hod mouse then every set of reals is Wadge reducible to a code of an iteration strategy. Notes by rds: Sargsyan.
  12. Ralf Schindler: Varsovian models with more Woodin cardinals. We report on joint work with Grigor Sargsyan. Varsovian models, II (1st part), Varsovian models, II (2nd part), Varsovian models, II (appendix), Varsovian models, II (appendix 2). Notes by Stefan Miedzianowski: Schindler, part 1 and 2.
  13. Farmer Schlutzenberg and Yizheng Zhu: Tutorial I on the derived model theorem. File: Schlutzenberg, notes by rds: Zhu, part 1 and 2.
  14. Farmer Schlutzenberg: Semiscales constructed from mice. Abstract: In approximately 1999, Neeman announced a construction of scales directly from mice, avoiding determinacy arguments. His work remains unpublished. We will describe a new construction which produces semiscales directly from mice. It yields, for example, Semiscale(Π13). Notes by rds: Schlutzenberg, part 1, Schlutzenberg, part 2.
  15. John Steel: Tutorial IV on lbr hod pairs and local HOD computation: propagating HPC past inductive-like classes, and models of LSA and stronger things from lbr hod pairs. Notes by rds: Steel, part 1, Steel, part 2. Slides: Steel, part 2.
  16. Nam Trang: An outline of the core model induction Abstract: We give a brief and nontechnical introduction to the core model induction. We describe how the core model induction works, what type of problems one can tackle with the core model induction, and the current state of the subject. Notes by rds: Trang, part 1, Trang, part 2
  17. Sandra Uhlenbrock: HOD in inner models with finitely many Woodin cardinals. Abstract: We analyze HOD in the inner model Mn(x,g) for reals x of sufficiently high Turing degree and a suitable generic g. This is joint work with Grigor Sargsyan. Notes by rds: Uhlenbrock
  18. Trevor Wilson: Martin's closure operation and scales on local Π21 sets. We develop some basic properties of the "closure operation" introduced by Martin that maps a pointclass S to S = { A : for every countable σ there is some A' in S such that A ∩ σ = A' ∩ σ }. Applying this operation to a local version of the pointclass OD gives an "envelope" pointclass that precisely describes the complexity of scales for the corresponding local version of Π21. Applications include (1) the Kechris-Woodin determinacy transfer theorem, which together with results of Steel establishes the pattern of scales in L(R), and (2) Woodin's result that the intersection of divergent models of AD+ satisfies "every set of reals is Suslin." Notes by rds: Wilson, part 1, Wilson, part 2, Wilson, part 3, Wilson, part 4, Wilson, part 5.

Problem session:

Problem list.

Participants:

Dominik Adolf (Münster) ₰ D
Juan P. Aguilera (TU Vienna)₰ K
Omer Ben-Neria (UCLA)₰ K
Mariam Beriashvili (Tbilisi)July 16--?Europa Haus
Douglas Blue (Harvard)₰ J
Fabiana Castiblanco (Münster)
Justin Cavitt (Harvard) ₰ G
Gabriel Fernandes (Münster)
Elliot Glazer (Rutgers)₰ G
Gabriel Goldberg (Harvard)July 16--Aug 05 (?)
Steve Jackson (Texas)July 23--Aug 01Handwerkskammer
Ronald Jensen (Berlin)July 29--Aug 06Hotel am Schloßpark
Martin Köberl (Rutgers)₰ G
Stefan Miedzianowski (Münster)
Bill Mitchell (Gainesville) July 17--Aug 05 Hotel Bakenhof + Hotel am Schloßpark
Dan Saattrup Nielsen (Bristol)₰ K
Menachem Magidor (Jerusalem)July 21--Aug 06 Europa Haus
Grigor Sargsyan (Rutgers)July 16--Aug 08Germania Campus
Ralf Schindler (Münster)
Farmer Schlutzenberg (Münster)
Benjamin Siskind (Berkeley)₰ J
John Steel (Berkeley) July 14--Aug 08Hotel am Schloßpark + Humboldt Haus
Nam Trang (UC Irvine)July 18--?Germania Campus
Sandra Uhlenbrock (Vienna)
Trevor Wilson (Miami Univ., Oxford OH)
Shi Xianghui (Beijing)
Yizheng Zhu (Münster)
Martin Zeman (UC Irvine) July 16--Aug 04Germania Campus



Housing information:

  • airbnb
  • Barbara's bed and breakfast, she has rooms for 25 -- 68 EUR. This is the only one not within walking distance, so you'd need a bike; but it's nice and cheap.
  • Nordstern hostel, rooms for 29 EUR.
  • My bed and breakfast, rooms for 49 -- 69 EUR.
  • Handwerkskammer Münster. They have very nice rooms for less than 100 € per week. See here. A highly recommended option! Contact: Frau Iris Weverinck-Friedrichs, iris.weverinck@hwk-muenster.de, phone no. +49-251-705-1305.
  • Haus Niemann, rooms for 59,50 EUR.
  • Factory Hotel.
  • Hotel am Schlosspark.
  • Hotel Jellentrup.

  • Travel information:

    Münster has an airport, IATA code: FMO. You may e.g. fly there with Lufthansa (or, United, operated by Lufthansa 😊) via Frankfurt or Munich. A cab from FMO to the center is about 50 €, but there are shuttle buses for about 7 €. Another good option to reach Münster is to fly to Düsseldorf, IATA code: DUS, and take a train from there, which takes about 1 1/2 hours.

    Tourist information:

    The fifth Sculpture Projects Münster, see here, will take place in 2017: Skulptur Projekte.