2011 seminar talk: Non-absoluteness of model existence for infinitary logic

Talk held by Martin Koerwien (KGRC) at the KGRC seminar on 2011-10-06.

Abstract

We discuss how much the notion '\(\sigma\) has a model of size \(\aleph_\alpha\)' (where \(\sigma\) is a sentence of \(L_{\omega_1,\omega}\)) can depend on set theoretic properties. After some general remarks and examples, we will focus on the presentation of a complete sentence for which model-existence in \(\aleph_3\) is non-absolute modulo ZFC+GCH.