David Marker : Montalban on Vaught's Conjecture

Posted by Lynn Scow , part of the Logic Seminar.

At

Sept. 18, 2012, 4 p.m.

In

SEO 427

Abstract

Antonio Montalban has proved (under the assumption of projective determinacy) that an $L_{\omega_1,\omega}$-sentence is a counterexample to Vaught's Conjecture if and only if there is a cone in the Turing degrees where every $X$-hyperarithmetic model has an $X$-recursive copy. I will give background material and describe Montalban's results.