Recent and upcoming talks by Andrés Caicedo

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…

Andrés Caicedo: Determinacy from large cardinals

Boise Set Theory Seminar Wednesday, January 30 Room: Math conference and break room Speaker: Andrés Caicedo Title: Determinacy from large cardinals: an overview Abstract: A game is determined when one of the players has a winning strategy. continue reading…