John Baldwin : Properties of counterexamples to Vaught's Conjecture

Posted by Matthias Aschenbrenner , part of the Logic Seminar.

At

Jan. 24, 2006, 4 p.m.

In

SEO 427

Abstract

We will discuss the results of Makkai and Harnik that every counterexample to the Vaught conjecture has an uncountable model; indeed it has both an uncountable model which is $\infty,\omega$-equivalent to a countable model and one which is not. We give an `admissible set free' proof of the first result. Further, we observe that any first order counterexample to Vaught's conjecture has $2^{\aleph_1}$ models of power $\aleph_1$.