## Samuel Coskey: Introduction to continuous logic

Wednesday, March 4 from 3 to 4pm
Room: Math 124
Speaker: Samuel Coskey (BSU)
Title: An introduction to continuous logic

Abstract: Continous logic is a proper generalization of first order logic where the usual binary truth values are replaced by the unit interval $[0,1]$. The models for this logic are metric structures, which are metric spaces together with continuous functions and $[0,1]$-valued relations. Just as ordinary logic has typical applications in discrete math, continuous logic has applications in analysis. In this talk we will introduce just the basic concepts and theory of continuous logic.

## Randall Holmes: Preliminaries for Proving the Consistency of NF

Wednesday, February 11 from 3 to 4pm
Room: Math 124
Speaker: Randall Holmes (BSU)
Title: Preliminaries for Proving the Consistency of NF

Abstract: We will discuss some preliminary machinery intended for use in a consistency proof of Quine’s set theory New Foundations.
No particular familiarity with New Foundations is presupposed.

## Samuel Coskey: Conjugacy and homogeneous graphs, II

Wednesday, February 4 from 3 to 4pm
Room: Math 124
Speaker: Samuel Coskey (BSU)
Title: Conjugacy and homogeneous graphs, II

Abstract: This talk is continued from last semester. We study the conjugacy relation on the automorphism group of a homogeneous structure from the point of view of Borel complexity theory. In particular, we present three examples of homogeneous graphs whose corresponding conjugacy problems have three different complexities.

## Andrés Caicedo: Topological partition properties of $\omega_1$, part II

Wednesday, January 28 from 3 to 4pm
Room: Math 124
Speaker: Andrés Caicedo (BSU)
Title: Some topological partition properties of $\omega_1$, part II

Abstract: We discuss some new results on the topological partition calculus of ordinals less than or equal to $\omega_1$. This is joint work with Jacob Hilton.

## Andrés Caicedo: Topological partition properties of $\omega_1$

Wednesday, January 21 from 3 to 4pm
Room: Math 124
Speaker: Andrés Caicedo (BSU)
Title: Some topological partition properties of $\omega_1$

Abstract: I present some classical and new positive results on the topological version of partition relations involving $\omega_1$. I also use the topic as an excuse to review some combinatorics of stationary sets, including Fodor’s lemma.

## Andrés Caicedo: Co-analytic uniformization

Wednesday, December 10 from 3 to 4pm
Room: Math 226
Speaker: Andrés Caicedo (BSU)
Title: Co-analytic uniformization

Abstract: It is an easy consequence of the axiom of choice that if X is an arbitrary set and R is a binary relation on X (a subset of $X^2$) then R admits a uniformization, that is, there is a function f whose domain is $\{x \in X : \text{there is a } y \in X \text{ with } x R y\}$ and such that for all x in its domain, x R f(x).

If X is the set of reals, and R is a reasonably definable relation, one might expect that the existence of such a function f can actually be established without using the axiom of choice.

We sketch a classical result independently due to Novikov and Kondo showing that this is indeed the case if R is Borel (and even if it is “slightly” more complicated than Borel).

## Andres Caicedo: Ramsely theory of very small countable ordinals II

Wednesday, October 1 from 3 to 4pm
Room: Math 226
Speaker: Andrés Caicedo (BSU)
Title: Ramsey theory of very small countable ordinals II

Abstract: We examine a closed version of the pigeonhole principle for ordinals, and use it to draw upper bounds on closed Ramsey numbers.

## Andrés Caicedo: Ramsey theory of very small countable ordinals

Wednesday, September 24 from 3 to 4pm
Room: Math 226
Speaker: Andrés Caicedo (BSU)
Title: Ramsey theory of very small countable ordinals

Abstract: We present a brief introduction to classical Ramsey theory, and discuss two extensions in the context of ordinals. We limit ourselves to small countable ordinals, emphasizing those smaller than $\omega^2$.

## Thomas Forster: WQOs and BQOs

Wednesday, September 10 from 3 to 4pm
Room: Math 226
Speaker: Thomas Forster (Cambridge)
Title: WQOs and BQOs – an Introductory Talk

Abstract: A WQO is a transitive reflexive relation with no infinite antichains and no infinite strictly descending chains. In this introductory talk (very few proofs!) for a general mathematical audience i shall try to show some of the many places that WQOs have spread their tentacles into, how they give rise to BQOs, the connections with finite combinatorics (Seymour-Robertson theorem), undecidability results in arithmetic and other fun stuff. I’ll even tell you what the two TLAs stand for.

## Samuel Coskey: Conjugacy and homogeneous graphs

Wednesday, September 3 from 3 to 4pm
Room: Math 226
Speaker: Samuel Coskey (BSU)
Title: Conjugacy and homogeneous graphs

Abstract: Before studying the conjugacy problem in a given Polish group G, it is natural to ask what is the complexity of the conjugacy equivalence relation. We study this relation in the case when G is the automorphism group of a homogeneous graph (directed or undirected). The homogeneous graphs have been classified by Cherlin and we will briefly run through the complete list. Then we will give examples where the complexity of the conjugacy relation on G is smooth, complete, and in between.