# Admissible Covers and Compactness Arguments for Ill-founded Models of Set Theory

Set theory seminarFriday, September 11, 201510:00 amGC 3212

# Admissible Covers and Compactness Arguments for Ill-founded Models of Set Theory

The Barwise compactness theorem is a powerful tool, allowing one to prove many interesting results which cannot be gotten just from the ordinary compactness theorem. For example, it can be used to show that every countable transitive model of set theory has an end extension which is a model of $V = L$.  However, the Barwise compactness theorem only applies to transitive sets. What are we to do if we want to have compactness arguments for ill-founded models of set theory?