Unreachability of $\Gamma_{2n+1,m}$

Speaker: 

Derek Levinson

Institution: 

UCLA

Time: 

Monday, November 27, 2023 - 4:00pm to 5:30pm

Host: 

Martin Zeman

Location: 

RH 340P

We prove from ZF + AD + DC that there is no sequence of distinct $\Gamma_{1,m}$ sets of length $\aleph_{m+2}$. This is the optimal result for the pointclass $\Gamma_{1,m}$ by earlier work of Hjorth. We also get a bound on the length of sequences of $\Gamma_{2n+1,m}$ sets using the same techniques.

Distality in continuous logic

Speaker: 

Aaron Anderson

Institution: 

UCLA

Time: 

Monday, November 13, 2023 - 4:00pm to 5:30pm

Host: 

Isaac M. Goldbring

Location: 

RH 306P

We examine distal theories and structures in the context of continuous logic, providing several equivalent definitions.

By studying the combinatorics of fuzzy VC-classes, we find continuous versions of (strong) honest definitions and distal cell decompositions.

By studying generically stable Keisler measures in continuous logic, we apply the theory of continuous distality to analytic versions of graph regularity.

We will also present some examples of distal metric structures, including dual linear continua and a continuous version of o-minimality.

The definability of the nonstationary ideal

Speaker: 

Ralf Schindler

Institution: 

Muenster University, Germany

Time: 

Monday, March 27, 2023 - 4:00pm to 5:30pm

Host: 

Martin Zeman

Location: 

RH 440R

We show that (a) PFA is consistent with having that NS_{\omega_1} is \Pi_1 definable and that (b) MM proves that NS_{\omega_1} is not \Pi_1 definable. Yet another time this shows that MM is the right generalization of MA. This is joint work with D. Asperó, S. Hoffelner, P. Larson, X. Sun, L. Wu.

Unreachability of Inductive-Like Pointclasses in L(R)

Speaker: 

Derek Levinson

Institution: 

UCLA

Time: 

Monday, January 23, 2023 - 4:00pm to 5:30pm

Host: 

Martin Zeman

Location: 

RH 440R

We will show there is no sequence of distinct Sigma^2_1 sets of length (delta^2_1)^+ in L(R). We also discuss how to prove an analogous result for any inductive-like pointclass in L(R). This is joint work with Itay Neeman and Grigor Sargsyan.

An inner model from stationary logic

Speaker: 

Jouko Vaananen

Speaker Link: 

http://www.math.helsinki.fi/logic/people/jouko.vaananen/

Institution: 

University of Helsinki

Time: 

Monday, November 28, 2022 - 4:00pm to 5:30pm

Host: 

Matthew D. Foreman (he/him/his)

Location: 

RH 440 R

Godel's constructible universe uses first order logic to build a model of ZFC containing all of the ordinals and where the GCH holds.  This talk describes a method of building analogous models using Stationary Logic. These are well-founded inner models of stronger axioms than ZFC that retain elements of fine structure. 

Stationary Logic is a stronger logic than first order logic, but retains desirable model theoretic aspects. 

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