Ioannis Souldatis : Title: Characterizing successor cardinals by $L_{\omega_1,\omega}$-sentences.

Posted by John Baldwin , part of the Logic Seminar.

At

Dec. 10, 2013, 3:30 p.m.

In

SEO 427

Abstract

An $L_{\omega_1,\omega}$ sentence $\phi$ characterizes a cardinal $\kappa$, if $\phi$ has models in all powers up to $\kappa$, but not in $\kappa^+$. During the talk we will focus on the results and the construction in Hjorth's [1], and state some extensions of these results, as well as questions that remain open. [1] Hjorth, G. Knight's model, its automorphism group, and characterizing the uncountable cardinals J. Math. Log., 2002, 2, 113-144