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Continuing earlier works of several authors, we investigate various relationships between finitary sentences, infinitary sentences, and the sets of countable models of sentences. In particular, we partially extend a result of Keisler [5] and some results of Vaught [22] and Miller [9] from the quantifier-alternation and difference hierarchies to finer hierarchies, and confirm two conjectures formulated by Wadge [23].

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\(L_{\omega \omega }\) , \(L_{\omega _1\omega }\) , and the Wadge Hierarchy

  • 会议论文

  • 发表日期：

    2025年

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  • Victor Selivanov

摘要

Continuing earlier works of several authors, we investigate various relationships between finitary sentences, infinitary sentences, and the sets of countable models of sentences. In particular, we partially extend a result of Keisler [5] and some results of Vaught [22] and Miller [9] from the quantifier-alternation and difference hierarchies to finer hierarchies, and confirm two conjectures formulated by Wadge [23].