Department of Mathematics

Mathematics 253-37 | Caltech
1200 E California Blvd | Pasadena, CA 91125
Tel: (626) 395-4335 | Fax: (626) 585-1728

Logic in Southern California

Saturday, February 20, 2016
2:00 - 6:00 pm
Sloan room 151

Funded by NSF grant DMS-1044150


2:00-3:00 Martino Lupini (Caltech)
3:15-4:15 Geoff Galgon (UCI)
4:15-5:00 Coffee Break
5:00-6:00 Spencer Unger (UCLA)

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Martino Lupini

Title: Weak equivalence of actions and first order logic

Abstract: I will present a model-theoretic perspective on the notion of weak equivalence for actions on the standard probability space. I will explain how this perspective allows one to recover some know results about the space of weak equivalence classes, and at the same time establish their noncommutative analogs.This is joint work with Peter Burton.

Geoff Galgon

Title: Perfect and Scattered Subsets of 2^{\kappa} and P_{\kappa}\lambda,
with an Application to Almost Disjoint Refinements

Abstract: The topological notions of perfectness and scatteredness can be
generalized in several ways to spaces like \kappa^{\kappa}, 2^{\kappa},
and P_{\kappa}\lambda. We present one possible way of doing this, and show
as an application how the consistency of a Cantor-Bendixson-like dichotomy
for closed subsets of \kappa^{\kappa} can be used to prove that in generic
extensions by a broad class of forcings, there is an almost disjoint
refinement of the ground model's \kappa-sized subsets of \kappa.

Spencer Unger

Title: Successive failures of weak square and the failure of SCH

Abstract: We are motivated by the question "Can one construct a kappa-Aronszajn tree for some kappa > aleph_1 in ZFC?"  Towards a negative answer, we prove the following theorem: From large cardinals it is consistent that aleph_{omega^2} is strong limit and there are no special kappa-Aronszajn trees for any regular kappa in the interval [aleph_2, aleph_{omega^2+2}].

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Directions and Parking:


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1200 E. California Blvd.
Pasadena, CA 91125

Take a look at the Caltech campus map

There is free Saturday parking in underground structure #126. Feel free to park in any of the commuter spaces (these are marked by a red line).

Talks will be held in Sloan building #37, Room 151 on the ground floor

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Alexander Kechris (Caltech). Organizer Information
Itay Neeman (UCLA). Organizer Information
Matthew Foreman (UCI). Organizer Information
Martin Zeman (UCI) Organizer Information

Local Organizers:

Alexander Kechris (Caltech) Organizer Information
Martino Lupini (Caltech) Organizer Information

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