We give a model theoretic proof, replacing admissible set theory by the Lopez-Escobar theorem, of Makkai's theorem: Every counterexample to Vaught's Conjecture has an uncountable model which realizes only countably many ℒ$_{ω₁,ω}$-types. The following result is new. Theorem: If a first-order theory is a counterexample to the Vaught Conjecture then it has 2\sp ℵ₁ models of cardinality ℵ₁.

We show that every ℵα can be characterized by the Scott sentence of some countable model; moreover there is a countable structure whose Scott sentence characterizes ℵ1 but whose automorphism group fails the topological Vaught conjecture on analytic sets. We obtain some partial information on Ulm type dichotomy theorems for the automorphism group of Knight's model.

For sentences $\phi$ of $L_{\omega_{1},\omega}$, we investigate the question of absoluteness of $\phi$ having models in uncountable cardinalities. We first observe that having a model in $\aleph_{1}$ is an absolute property, but having a model in $\aleph_{2}$ is not as it may depend on the validity of the continuum hypothesis. We then consider the generalized continuum hypothesis context and provide sentences for any $\alpha\in\omega_{1}\setminus\{0,1,\omega\}$ for which the existence of a model in $\aleph_{\alpha}$ is nonabsolute . Finally, we present a complete (...) sentence for which model existence in $\aleph_{3}$ is nonabsolute. (shrink)