IN SOUTHERN CALIFORNIA
Saturday, May 21st, 2016
UCLA Math Sciences 6627
Funded by NSF Grant DMS-1044604
2:00 - 3:00 Ronnie Chen (Caltech), Structurable equivalence relations.
3:15 - 4:15 Garrett Ervin (UC-Irvine), Every linear order isomorphic to its cube is isomorphic to its square.
4:45 - 5:45 Bill Chen (UCLA), Can mutual and tight stationarity agree anywhere?
Abstracts Driving directions and parking Organizers Previous meetings
Abstracts of the talks:
Ronnie Chen: Structurable equivalence relations.
For a class K of countable structures, a countable Borel equivalence relation is K-structurable if there is a Borel way to put a structure in K on each equivalence class. We will present some results in the abstract theory of structurable equivalence relations, including: their relationship with various kinds of Borel homomorphisms and reductions; the order-theoretic structure of the poset of classes of K-structurable equivalence relations for various K; and the relevance of certain model-theoretic properties of the class K. This is joint work with Alexander Kechris.
Garrett Ervin: Every linear order isomorphic to its cube is isomorphic to its square.
In the early 1950s, Sierpinski asked whether there exists a linear order
that is isomorphic to its lexicographically ordered cube but not
isomorphic to its square. The analogous question, whether for a given
class of structures \(C\), there exists \(X\in C\)
isomorphic to \(X^3\) but not to
\(X^2\), has been answered positively for many different classes of structures,
including groups, Boolean algebras, topological spaces, graphs, partial
orders, and Banach spaces. However, the answer to Sierpinski's question
turns out to be negative: any linear order that is isomorphic to its cube
is isomorphic to its square, and thus to all of its finite powers. I will
present an outline of the proof and give some related results.
Bill Chen: Can mutual and tight stationarity agree anywhere?
Mutual and tight stationarity are two notions of stationarity defined
on certain products associated to a singular cardinal, introduced by
Foreman and Magidor. Tight stationarity is closely related to the
structure of scales at the singular cardinal, whereas mutual stationarity
has a more mysterious, model-theoretic character. In this talk, I will
investigate the question of Cummings, Foreman, and Magidor of whether
every mutually stationary sequence can be tightly stationary.
The main result is a model where mutual and tight stationarity are
distinct everywhere, and where this property is quite indestructible
under further forcing (based on joint work with Itay Neeman).
Driving directions and parking:
From the 405 North
From the 405 South
From the east via the 10 (Santa Monica Freeway)
To park on campus you will need to purchase a daily parking permit at the Information & Parking Booth. The nearest parking lots to the Department of Mathematics are 9, 8, and 2.
Organizers: Alexander Kechris, Itay Neeman, Martin Zeman
Caltech, February 20, 2016
UCI, November 14, 2015
Caltech, March 7, 2015
UCLA, November 15, 2014
UCI, May 10, 2014
Caltech, March 8, 2014
UCLA, November 16, 2013
UCLA, June 1, 2013
UCI, February 23, 2013
Caltech, November 17, 2012
UCLA, May 12, 2012
Caltech, February 18, 2012
UCI December 3, 2011