An undecidable extension of Morley's theorem on the number of countable models

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2023-10-01 DOI:10.1016/j.apal.2023.103317

Christopher J. Eagle , Clovis Hamel , Sandra Müller , Franklin D. Tall

引用次数: 0

Abstract

We show that Morley's theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of equivalence relations obtained by countable intersections of projective sets in several models of set theory. Our methods include random and Cohen forcing, Woodin cardinals and Inner Model Theory.

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莫雷定理关于可数模型数的不可定推广

我们证明了Morley关于可数一阶理论的可数模型数的定理在推广到二阶逻辑时变成了不可判定的陈述。更一般地说，我们计算了在集合论的几个模型中，通过投影集的可数交集获得的等价关系的等价类的数量。我们的方法包括随机和Cohen强迫，Woodin基数和内部模型理论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.