# 2015 seminar talk: Unfoldable cardinals and some related problems

Talk held by Franqui Solis Cárdenas Poloche (Universidad Nacional de Colombia) at the KGRC seminar on 2015-01-22.

### Abstract

Unfoldable cardinals are between weakly compact cardinals and Ramsey cardinals but they still relativize to $L$. However unfoldable cardinals resemble in some aspects to large large cardinals like strongly compact cardinals. In this talk I would like to present two aspects of this. Weakly compact cardinals limit of unfoldable cardinals are unfoldable cardinals and if $K$ is an AEC with $LS(K) < \kappa$ for $\kappa$ a $\theta$ unfoldable cardinal then $K$ is $(\kappa,\theta)$ tame for $\kappa$ short types.