CUNY Graduate Center
Hybrid (email Victoria Gitman for meeting id)
Room 6496
Fridays 11:00am-12:30pm
Organized by Gunter Fuchs and Victoria Gitman
Calendar
February 7
Hybrid (email Victoria Gitman for meeting id)
11:00am NY time
Room: 6496
Ali Enayat
University of Gothenburg
Models of set theory: extensions and dead-ends
Abstract
This is a two-part talk concerning existence/non-existence of certain kinds of extensions of arbitrary models of ZF, with no regard to countability or well-foundedness of the models involved. The talk is based a recent preprint: arXiv:2406.14790v1. The results presented include the following two. In Theorem A below, N is said to be a conservative elementary extension of M if N is an elementary extension of M with the property that the intersection of every parametrically definable subset of N with M is parametrically definable in M.
Theorem A. Every model M of ZF with a definable global well-ordering has a conservative elementary extension N that contains an ordinal above all of the ordinals of M.
Theorem B. Every consistent extension of ZF has a model of power aleph_1 that has no end extension to a model of ZF.
Slides
Video
February 14
Hybrid (email Victoria Gitman for meeting id)
11:00am NY time
Room: 6496
Ali Enayat
University of Gothenburg
Models of set theory: extensions and dead-ends part II
Abstract
This is a two-part talk concerning existence/non-existence of certain kinds of extensions of arbitrary models of ZF, with no regard to countability or well-foundedness of the models involved. The talk is based a recent preprint: arXiv:2406.14790v1. The results presented include the following two. In Theorem A below, N is said to be a conservative elementary extension of M if N is an elementary extension of M with the property that the intersection of every parametrically definable subset of N with M is parametrically definable in M.
Theorem A. Every model M of ZF with a definable global well-ordering has a conservative elementary extension N that contains an ordinal above all of the ordinals of M.
Theorem B. Every consistent extension of ZF has a model of power aleph_1 that has no end extension to a model of ZF.
Slides
Video
February 28
Hybrid (email Victoria Gitman for meeting id)
11:00am NY time
Room: 6496
Andreas Lietz
TU Wien
Equiconsistencies involving strengthenings of PFA
Abstract
We discuss the famous open problem of determining the exact consistency strength of PFA. We present an equiconsistency between Ben Goodman's Sigma_n-Correct Proper Forcing Axiom, which implies PFA, and supercompact for C^(n-1)-cardinals under additional mild assumptions for large enough n. Without these assumptions we can prove a dichotomy resembling Woodin's HOD dichotomy with a model containing the mantle taking on the role of HOD.
Video
March 7
Hybrid (email Victoria Gitman for meeting id)
11:00am NY time
Room: 6496
Tom Benhamou
Rutgers University
TBA
Abstract
March 21
Hybrid (email Victoria Gitman for meeting id)
11:00am NY time
Room: 6496
Tristan van der Vlugt
TU Wien
TBA
Abstract
April 4
Hybrid (email Victoria Gitman for meeting id)
11:00am NY time
Room: 6496
Siiri Kivimäki
University of Helsinki
TBA
Abstract
Previous Semesters