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arXiv · 2107.07636

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

Christopher J. Eagle·Clovis Hamel·Sandra Müller·Franklin D. Tall
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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 $\sigma$-projective equivalence relations in several models of set theory. Our methods include random and Cohen forcing, Woodin cardinals and Inner Model Theory.

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BibTeXRIS

Christopher J. Eagle, Clovis Hamel, Sandra Müller, Franklin D. Tall. 2021-07-15. An undecidable extension of Morley's theorem on the number of countable models. https://arxiv.org/abs/2107.07636

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