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.

October 19, 2007

Speaker: Brandon Seward (UNT)

Title: A coloring property for countable groups, part 2

October 12, 2007

Speaker: Brandon Seward (UNT)

Title: A coloring property for countable groups, part 1

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 talk covers

joint work with Dr. Gao and Dr. Jackson in identifying groups which have the

coloring property. We will review some of our earlier results as well as present

more recent developements.

September 28, 2007

Speaker: Dan Walker (UNT)

Title: An introduction to non-standard analysis, Part II

September 21, 2007

Speaker: Dan Mauldin (UNT)

Title: Selection and separation theorems and problems for probability measures

Abstract: Let X be a Polish space and let Pr(X) be the Polish space of probability

measures defined on the Borel subsets of X in the weak* topology. The "first

support separation" theorem (proven by myself, Priess and Weizsacker) for
probability measures states that if A₁ and A₂ are two analytic sets of probability
measures such that A₁ and A₂ are measure convex and each measure in A₁
is singular or orthogonal to each measure in A₂, then there is a Borel set B in X

such that each measure in A₁ is supported on B and each measure in A₂ is

supported on the complement of B. This separation theorem does not necessarily

hold if we do not assume the sets are measure convex. I will describe an example

due to Blackwell illustrating this. I will describe what sort of separation one can get

using Martin's axiom and some applications to the existence of a "perfect statistic" for
probability transition kernels. Finally I will discuss some still unsolved problems

concerning this circle of ideas.

September 14, 2007

Speaker: Dan Walker (UNT)

Title: An introduction to non-standard analysis

Abstract: We will develop the notion of non-standard analysis, which is a way of

formulating classical analysis on R without the use of limits. Central to this idea is

the construction of R*, the set of hyperreal numbers, which is a linearly ordered

field properly extending R. We will present the non-standard definitions for familiar

concepts such as convergent sequences, continuous functions, derivatives, and

integration, and show that they are equivalent to the standard definitions. If there is

time, we will see under what circumstances second-order sentences in the theory of

R "transfer" to R*.