Maximal models up to the first measurable in ZFC

Abstract

Theorem: There is a {\em complete sentence} $\varphi$ of $L_{{\omega }_1,\omega }$ such that $\varphi$ has maximal models in a set of cardinals $\lambda$ that is cofinal in the first measurable $\mu$ while $\varphi$ has no maximal models in any $\chi \ge \mu$.

27 pages