Kurt Gödel Research Center

2012 seminar talk: Large Properties at Small Cardinals

Talk held by Laura Fontanella (KGRC) at the KGRC seminar on 2012-10-18.

Abstract

One of the most intriguing research areas is the study of properties associated with large cardinals, that can be satisfied by small cardinals as well. The tree property is a notable example of such properties. Indeed, an inaccessible cardinal is weakly compact if and only if it satisfies the tree property. Strongly compact and supercompact cardinals admit a similar characterization in terms of combinatorial properties. An inaccessible cardinal is strongly compact if and only if it satisfies the strong tree property; it is supercompact if and only is it satisfies the super tree property. We discuss some consistency results concerning the strong and super tree properties at small cardinals.