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arXiv · 1903.09753

The number of models of a fixed Scott rank, for a counterexample to the analytic Vaught conjecture

Paul Larson·Saharon Shelah
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Abstract

We show that if $\gamma \in \omega \cup \{\aleph_{0}\}$ and $\mathcal{A}$ is a counterexample to the analytic Vaught conjecture having exactly $\gamma$ many models of Scott rank $\omega_{1}$, then there exists a club $C \subseteq \omega_{1}$ such that $\mathcal{A}$ has exactly $\gamma$ many models of Scott rank $\alpha$, for each $\alpha \in C$.

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Paul Larson, Saharon Shelah. 2019-03-23. The number of models of a fixed Scott rank, for a counterexample to the analytic Vaught conjecture. https://arxiv.org/abs/1903.09753

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