The classification of countable models of set theory

Mathematical Logic Quarterly 66 (2):182-189 (2020)
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Abstract

We study the complexity of the classification problem for countable models of set theory (). We prove that the classification of arbitrary countable models of is Borel complete, meaning that it is as complex as it can conceivably be. We then give partial results concerning the classification of countable well‐founded models of.

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Citations of this work

Equivalence of generics.Iian B. Smythe - 2022 - Archive for Mathematical Logic 61 (5):795-812.

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References found in this work

Infinite time Turing machines.Joel David Hamkins & Andy Lewis - 2000 - Journal of Symbolic Logic 65 (2):567-604.
Models and types of Peano's arithmetic.Haim Gaifman - 1976 - Annals of Mathematical Logic 9 (3):223-306.
Infinite time Turing machines.Joel David Hamkins & Andy Lewis - 2000 - Journal of Symbolic Logic 65 (2):567-604.
Model Theory: An Introduction.David Marker - 2003 - Bulletin of Symbolic Logic 9 (3):408-409.

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