Gabriel Fernandes

Tall cardinals in extender models

Gitik proved under ¬0^sword that if κ is a measurable cardinal and 2^κ > λ ≥ κ^+ and λ is a regular cardinal then o^K(κ) ≥ λ, where K stands for the core model. In joint work with Ralf Schindler, in a attempt to generalize Gitik’s result to larger core models, we obtained for the case where V is an extender model a characterization of λ-tall cardinals in terms of the function o^K(). In the talk I will define λ-tall cardinals, o^K(), give an informal definition of the core model, state precisely the characterization we obtained and sketch its proof.