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2nd Conference on
the core model induction and hod mice
Institut für Mathematische Logik, WWU Münster,
August 08 -- 19, 2011
This conference will be a sequel to the first Conference on the core model induction and hod mice that was held in Münster July 19 -- August 06, 2010.
Again, 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 formally 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, evenings, and weekends.
The conference organizers gratefully acknowledge financial support from the NSF (National Science Foundation, grant no. DMS-0801189, amendment no. 002), from the DFG (Deutsche Forschungsgemeinschaft, grant no. SCHI 484/3-1, and from the Marianne and Dr. Horst Kiesow-Stiftung, Frankfurt a.M.
Location: The talks will take place in the new building of our department (which is an annex to the old one), Orleansring 10, rooms no. N 1 and N 2 (ground floor).
The conference picture may be found below.
List of speakers, titles, and abstracts
David Aspero (Bogota): Measuring and CH. (had to be cancelled)
Andres Caicedo (Boise): Pmax consequences beyond
H(omega2).
Steve Jackson (Denton): The scale property from AD.
Grigor Sargsyan (Los Angeles/Rutgers): On
the strength of failure of square at singular strong limit
cardinal.
Abstract: We show that the the failure
of square at a singular strong
limit cardinal implies that there is a model of ADR
+ Θ is regular
containing the reals and ordinals.
John Krueger (Denton): A remark on the
non-compactness of square.
Ralf Schindler (Münster): The strength of BPFA plus a precipitous ideal on ω1.
Abstract: We show that a (slight?) strengthening of
BPFA together with the existence of a precipitous ideal on ω1
yields projective determinacy. A key step is to prove that K computes
successors of cardinals correctly if they carry a precipitous ideal.
This is joint work with B. Claverie.
Farmer Schlutzenberg (Denton, TX):
An alternate proof of Semiscale(Π13) from mice.
Neeman gave a construction of scales for many pointclasses from mice, via
his premouse lightening. I'll give an alternate construction of semiscales
from mice, for sufficiently closed pointclasses. It's unknown whether this
construction does give scales.
John Steel (Berkeley): PFA implies AD in L(R).
Nam Trang (Berkeley): The HOD computation in natural models of AD+.
We compute the full HOD of models satisfying AD+ + V = L(P(R))
under the
assumption that there is no model M satisfying ADR + Θ is
regular and
P(R)M ≠ P(R).
Philip Welch (Bristol): Determinacy in strong cardinals models.
Trevor Wilson (Berkeley): The strength of properties of ideals in the
Pmax extension of a
model of ADR + Θ regular.
Zhu Yizheng (Singapore): Every AD+ model below ADR + θ regular is a derived model of a premouse
Abstract:
We show that assuming AD+ + V=L(P(R))
and that there is no proper class
inner model containing all the reals and satisfying ADR + θ
regular, we can
force a premouse N so that V is a derived model of N. This work is based on hod mice
theory and earlier results along this line, part of which were done at the 1st
conference last year.
Martin Zeman (Irvine): Reconstructing extenders.
Abstract: We show that a (slight?) strengthening of BPFA together with the existence of a precipitous ideal on ω1 yields projective determinacy. A key step is to prove that K computes successors of cardinals correctly if they carry a precipitous ideal. This is joint work with B. Claverie.
Farmer Schlutzenberg (Denton, TX):
An alternate proof of Semiscale(Π13) from mice.
Neeman gave a construction of scales for many pointclasses from mice, via
his premouse lightening. I'll give an alternate construction of semiscales
from mice, for sufficiently closed pointclasses. It's unknown whether this
construction does give scales.
John Steel (Berkeley): PFA implies AD in L(R).
Nam Trang (Berkeley): The HOD computation in natural models of AD+.
We compute the full HOD of models satisfying AD+ + V = L(P(R))
under the
assumption that there is no model M satisfying ADR + Θ is
regular and
P(R)M ≠ P(R).
Philip Welch (Bristol): Determinacy in strong cardinals models.
Trevor Wilson (Berkeley): The strength of properties of ideals in the
Pmax extension of a
model of ADR + Θ regular.
Zhu Yizheng (Singapore): Every AD+ model below ADR + θ regular is a derived model of a premouse
Abstract:
We show that assuming AD+ + V=L(P(R))
and that there is no proper class
inner model containing all the reals and satisfying ADR + θ
regular, we can
force a premouse N so that V is a derived model of N. This work is based on hod mice
theory and earlier results along this line, part of which were done at the 1st
conference last year.
Martin Zeman (Irvine): Reconstructing extenders.
Nam Trang (Berkeley): The HOD computation in natural models of AD+.
We compute the full HOD of models satisfying AD+ + V = L(P(R)) under the assumption that there is no model M satisfying ADR + Θ is regular and P(R)M ≠ P(R).
Philip Welch (Bristol): Determinacy in strong cardinals models.
Trevor Wilson (Berkeley): The strength of properties of ideals in the
Pmax extension of a
model of ADR + Θ regular.
Zhu Yizheng (Singapore): Every AD+ model below ADR + θ regular is a derived model of a premouse
Abstract:
We show that assuming AD+ + V=L(P(R))
and that there is no proper class
inner model containing all the reals and satisfying ADR + θ
regular, we can
force a premouse N so that V is a derived model of N. This work is based on hod mice
theory and earlier results along this line, part of which were done at the 1st
conference last year.
Martin Zeman (Irvine): Reconstructing extenders.
Martin Zeman (Irvine): Reconstructing extenders.
Schedule:
| Mo, Aug 08 | Tue, Aug 09 | We, Aug 10 | Thu, Aug 11 | Fr, Aug 12 | |
| 9:30--11:00 | Schindler | Caicedo | Wilson/Steel | Wilson/Steel | Wilson/Steel |
| 11:30--12:30 | Schindler | Caicedo | Wilson/Steel | Wilson/Steel | Wilson/Steel |
| 14:30--16:00 | Nam Trang | Jackson | Krueger | Zeman | Sargsyan |
| 16:30--17:30 | Nam Trang | Nam Trang | Nam Trang | Zeman | Sargsyan |
| 17:30--∞ | Problems and Discussions | Problems and Discussions | Problems and Diskussions | Problems and Discussions | free |
| Mo, Aug 15 | Tue, Aug 16 | We, Aug 17 | Thu, Aug 18 | Fr, Aug 19 | |
| 9:30--11:00 | Sargsyan | Wilson | Sargsyan | Schlutzenberg | Sargsyan |
| 11:30--12:30 | Sargsyan | Wilson | Sargsyan | Schlutzenberg | Sargsyan |
| 14:30--16:00 | Zhu | Zhu | Zhu | Welch | free |
| 16:30--17:30 | Zhu | Zhu | Zhu | Sargsyan | free |
| 17:30--∞ | Problems and Discussions | Problems and Discussions | Problems and Diskussions | Problems and Discussions | free |
Accomodation:
Please make your reservations as soon as possible. Our conference will take place during vacation time in Nordrhein-Westfalen, and the hotels in Münster are usually booked out quite early. There will be no rooms in the student dormitories available this time!!!Participants:
| Dominik Adolf (Münster) | ||
| David Aspero (Bogota) | Aug 06--13 | Handwerkskammer |
| Andrés Caicedo (Boise) | July + Aug | arranged |
| Daisuke Ikegami (Helsinki) | Aug 06 -- 20 | Handwerkskammer |
| Steve Jackson (Texas) | Aug 07 -- 19 | Handwerkskammer |
| Richard Ketchersid | ??? | Handwerkskammer |
| Marios Koulakis (Münster) | ||
| John Krueger (Texas) | Aug 07 -- 14 | Hotel am Schlosspark |
| Bill Mitchell (Gainesville) | Aug 05 -- 20 | Handwerkskammer |
| Grigor Sargsyan (UCLA/Rutgers) | Zumsandestr. 28 | |
| Ernest Schimmerling (CMU) | Aug 06--20 | Handwerkskammer |
| Ralf Schindler (Münster) | ||
| Philipp Schlicht (Bonn) | OK | arranged |
| Farmer Schlutzenberg (Texas) | Aug 05 -- 20 | Handwerkskammer |
| John Steel (Berkeley) | Aug 01--19 | Germania Campus |
| Nam Trang (Berkeley) | Aug 06--19 | Germania Campus |
| Philip Welch (Bristol) | Aug 07--19 | Germania Campus |
| Trevor Wilson (Berkeley) | Aug 06--20 | Humboldt--Haus |
| Zhu Yizheng (Singapore) | Aug 06--19 | Germania Campus |
| Martin Zeman (Irvine) | Aug 07--19 | Germania Campus |
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