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ON SEPARATING WHOLENESS AXIOMS

Part of: Set theory Proof theory and constructive mathematics

Published online by Cambridge University Press:  12 March 2025

HANUL JEON Open the ORCID record for HANUL JEON [Opens in a new window]
HANUL JEON*
Affiliation:
DEPARTMENT OF MATHEMATICS CORNELL UNIVERSITY ITHACA, NY 14853 USA URL: https://hanuljeon95.github.io
*
E-mail: [email protected]
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Abstract

In this paper, we show that $\mathsf {ZFC}+\mathsf {WA}_{n+1}$ implies the consistency of $\mathsf {ZFC}+\mathsf {WA}_n$ for $n\ge 0$. We also prove that $\mathsf {ZFC}+\mathsf {WA}_n$ is finitely axiomatizable, and $\mathsf {ZFC}+\mathsf {WA}$ is not finitely axiomatizable unless it is inconsistent.

Keywords

wholeness axiomelementary embeddinglarge cardinalWAfinite axiomazability

MSC classification

Primary: 03E55: Large cardinals
Secondary: 03F05: Cut-elimination and normal-form theorems
Type
Article
Information
The Journal of Symbolic Logic , First View , pp. 1 - 24
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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