The Classification of Countable Models of Set Theory

John Clemens; Samuel Coskey; Samuel Dworetzky

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

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
Journal	Mathematical Logic Quarterly
State	Published - 1 Jul 2020

EGS Disciplines

Mathematics
Set Theory

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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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TY - JOUR

T1 - The Classification of Countable Models of Set Theory

AU - Clemens, John

AU - Coskey, Samuel

AU - Dworetzky, Samuel

PY - 2020/7/1

Y1 - 2020/7/1

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://scholarworks.boisestate.edu/math_facpubs/231

M3 - Article

SN - 0942-5616

JO - Mathematical Logic Quarterly

JF - Mathematical Logic Quarterly

ER -

The Classification of Countable Models of Set Theory

Abstract

EGS Disciplines

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