Categoricity-like Properties in the First Order Realm

Authors

DOI:

https://doi.org/10.36253/jpm-2934

Keywords:

Solidity, Tightness, Internal categoricity, Schemes, Biinterpretability, Retract, Nonstandard models, Peano Arithmetic, ZF

Abstract

By classical results of Dedekind and Zermelo, second order logic imposes categoricity features on Peano Arithmetic and Zermelo-Fraenkel set theory. However, we have known since Skolem’s anti-categoricity theorems that the first order formulations of Peano Arithmetic and Zermelo- Fraenkel set theory (i.e., PA and ZF) are not categorical. Here we investigate various categoricity-like properties (including tightness, solidity, and internal categoricity) that are exhibited by a distinguished class of first order theories that include PA and ZF, with the aim of understanding what is special about canonical foundational first order theories.

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Published

2024-09-10

How to Cite

Enayat, A., & Łełyk, M. (2024). Categoricity-like Properties in the First Order Realm. Journal for the Philosophy of Mathematics, 1, 63–98. https://doi.org/10.36253/jpm-2934

Issue

Vol. 1 (2024)

Section

Articles

License

Copyright (c) 2024 Ali Enayat, Mateusz Łełyk

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