# 2011 seminar talk: Non-absoluteness of model existence for infinitary logic, Part 2

Talk held by Martin Koerwien (KGRC) at the KGRC seminar on 2011-10-20.

### 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.