UNT Logic Seminar

UNTLS is an informal, participating seminar devoted to the research of foundations
of mathematics. The talks cover a variety of topics, ranging from introduction
to basics to presentation of recent research advances. Some of the talks will
not be very different from graduate classes; others are in workshop style.

April 20, 2007

Speaker: Su Gao (UNT)

Title: Coloring properties of countable groups (continued)

April 13, 2007

Speaker: Su Gao (UNT)

Title: Coloring properties of countable groups

Abstract:

We say that a countable group G has the coloring property if there is a

{0,1}-coloring c on G such that for all s in G there is a finite subset T of G

so that for all g in G there is t in T with c(gt) different from c(gst). This

seminar is a workshop on the following question: does every countable

group have the coloring property? I will talk about the motivation for this

concept, what we know about the question so far, and what needs to be

done to answer the question completely.

March 2, 2007

Speaker: Bunyamin Sari (UNT)

Title: The poset of spreading models as a Borel order (continued)

February 23, 2007

Speaker: Bunyamin Sari (UNT)

Title: The poset of spreading models as a Borel order

Abstract: This talk is concerned with the order structure of the set of

spreading models of a Banach space (generated by weakly null sequences),

where the order is the usual domination of bases. In particular, I will present

a recent solution of a problem (posed in our joint work with Dilworth and

Odell) by P. Dodos. It turned out that one needs to look at this structure as

a Borel order and use Descriptive Set Theory tools. This is one excellent

example of showing the importance of communication between different

areas of mathematics.

January 26, 2007

Speaker: Su Gao (UNT)

Title: A compactness theorem for complete sections (continued)

January 19, 2007

Speaker: Su Gao (UNT)

Title: A compactness theorem for complete sections

Abstract: A complete section for an equivalence relation is a set which meets

every equivalence class. Descreasing sequences of Borel complete sections

with an empty intersection play an important role in hyperfiniteness proofs.

In this talk (or series of talks) I will consider the shift action of Z on 2^Z and

prove a "compactness" theorem on its free part. The theorem states that a

decreasing sequence of closed complete sections must have a non-empty

intersection.