Recent and upcoming talks by Andrés Caicedo

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…

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. continue reading…

Andrés Caicedo: An absoluteness result

Tuesday, February 18 from 2 to 3pm Room: Mathematics 136 Speaker: Andrés Caicedo (BSU) Title: An absoluteness result Abstract: We present examples of some (Ramsey-theoretic) theorems of ZFC (whose standard proofs make blatant use of choice) that can be established in ZF as well. continue reading…

Andrés Caicedo: Second incompleteness

Monday, October 7 from 3 to 4pm Room: Mathematics 136 Speaker: Andrés Caicedo (BSU) Title: Second incompleteness Abstract: We sketch an essentially model theoretic proof (due to Woodin) of the second incompleteness theorem for ZF. continue reading…

Andrés Caicedo: Finitary mathematics

Thursday, February 21 from 1:30 to 2:30pm Room: B-309 Speaker: Andrés Caicedo Title: Finitary mathematics Abstract: $\mathsf{ZF}_{\mathsf{fin}}$ is the standard formalization of finitary mathematics; it replaces the axiom of infinity in $\mathsf{ZF}$ with its negation. continue reading…

Andres Caicedo: Determinacy from large cardinals II

Boise Set Theory Seminar Thursday, February 7 Room: B-309 Speaker: Andrés Caicedo (Boise State) Title: Determinacy from large cardinals: an overview II Abstract: We recall the definition of Woodin cardinals, and explain why they play a key role in proofs of determinacy. continue reading…