The Classification of Countable Models of Set Theory

John Clemens; Samuel Coskey; Samuel Dworetzky

doi:10.1002/malq.201900008

The Classification of Countable Models of Set Theory

John Clemens, Samuel Coskey, Samuel Dworetzky

Mathematics Department

Boise State University

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Abstract

We study the complexity of the classification problem for countable models of set theory ((Formula presented.)). We prove that the classification of arbitrary countable models of (Formula presented.) 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 (Formula presented.).

Original language	American English
Pages (from-to)	182-189
Number of pages	8
Journal	Mathematical Logic Quarterly
Volume	66
Issue number	2
DOIs	https://doi.org/10.1002/malq.201900008
State	Published - 1 Jul 2020

EGS Disciplines

Mathematics
Set Theory

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https://scholarworks.boisestate.edu/math_facpubs/231License: Other

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title = "The Classification of Countable Models of Set Theory",

abstract = "We study the complexity of the classification problem for countable models of set theory ((Formula presented.)). We prove that the classification of arbitrary countable models of (Formula presented.) 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 (Formula presented.).",

author = "John Clemens and Samuel Coskey and Samuel Dworetzky",

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AU - Coskey, Samuel

AU - Dworetzky, Samuel

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N2 - We study the complexity of the classification problem for countable models of set theory ((Formula presented.)). We prove that the classification of arbitrary countable models of (Formula presented.) 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 (Formula presented.).

AB - We study the complexity of the classification problem for countable models of set theory ((Formula presented.)). We prove that the classification of arbitrary countable models of (Formula presented.) 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 (Formula presented.).

UR - https://www.scopus.com/pages/publications/85087212828

U2 - 10.1002/malq.201900008

DO - 10.1002/malq.201900008

M3 - Article

SN - 0942-5616

VL - 66

SP - 182

EP - 189

JO - Mathematical Logic Quarterly

JF - Mathematical Logic Quarterly

IS - 2

ER -

The Classification of Countable Models of Set Theory

Abstract

EGS Disciplines

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