# Recent and upcoming talks by Andrés Caicedo

## Andres Caicedo: MRP and squares, II

Thursday, March 23, 2017, from 4 to 5:30pm East Hall, room 3088 Speaker: Andres Caicedo (Math Reviews) Title: MRP and squares, II Abstract: Justin Moore’s mapping reflection principle (MRP) seems to capture the consistency strength of PFA, since it implies the failure of square. continue reading…

## Andres Caicedo: MRP and squares

Thursday, March 16, 2017, from 4 to 5:30pm East Hall, room 2866 Speaker: Andres Caicedo (Math Reviews) Title: MRP and squares Abstract: Justin Moore’s mapping reflection principle (MRP) seems to capture the consistency strength of PFA, since it implies the failure of square. continue reading…

## Andres Caicedo: Preserving sequences of stationary subsets of omega_1

Thursday, November 10, 2016, from 4 to 5:30pm East Hall, room 3096 Speaker: Andres Caicedo (Math Reviews) Title: Preserving sequences of stationary subsets of omega_1 Abstract: Let M be an inner model that computes omega_1 correctly. continue reading…

## Andrés Caicedo: Topological partition calculus of countable ordinals

Thursday, April 14, 2016; 4:00-5:30 PM, in East Hall 2866. This is joint work with Jacob Hilton. We considered the topological version of the partition calculus in the setting of countable ordinals: Given ordinals $\alpha,\beta_0,\beta_1$, we say that $\alpha\to_{top}(\beta_0,\beta_1)^2$ iff for any 2-coloring of the edges of the complete graph on $\alpha$ vertices, for some color $i$, there is a complete monochromatic graph in color $i$ whose set of vertices is homeomorphic to $\beta_i$. continue reading…

## Andrés Caicedo: The Haddad-Sabbagh results in the partition calculus of small countable ordinals, II

Thursday, October 22, 1015 — 16:00 to 17:30 — East Hall 3096 We present the second part of a survey of results announced 45 years ago by Haddad and Sabbagh on the partition calculus of ordinals. continue reading…

## Andrés Caicedo: The Haddad-Sabbagh results in the partition calculus of small countable ordinals

Wednesday, October 7, 16:00 to 17:30 in 3096 East Hall We present a survey of results announced 45 years ago by Haddad and Sabbagh on the partition calculus of ordinals. Part of the interest in these results is that they are obtained by reducing genuine infinitary combinatorics problems to purely finite (albeit unfeasible) ones. continue reading…

## 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 $\omega_1$. continue reading…

## 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 $\omega_1$. continue reading…

## 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). continue reading…

## 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. continue reading…