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

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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Abstract

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

Original language	American English
Pages (from-to)	182-189
Number of pages	8
Journal	Mathematical Logic Quarterly
Volume	66
Issue number	2
Early online date	17 Jul 2020
DOIs	https://doi.org/10.1002/malq.201900008
State	Published - 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 (ZFC). We prove that the classification of arbitrary countable models of ZFC 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 ZFC.",

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AU - Dworetzky, Samuel

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

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

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

U2 - 10.1002/malq.201900008

DO - 10.1002/malq.201900008

M3 - Article

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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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