David Marker : Uncountable models of counterexamples to Vaught's Conjecture

Posted by David E. Marker , part of the Logic Seminar.

At

June 30, 2011, 9:30 a.m.

In

SEO 612

Abstract

I will begin by surveying some of the known results on uncountable models of counterexamples to Vaught's Conjecture for $L_{\omega_1,\omega}$-sentences and then give a sketch of an unpublished result of Leo Harrington showing that counterexamples have models of unbounded Scott rank below $\omega_2$. In particular this shows that a counterexample has at least $\aleph_2$ models of size $\aleph_1$.