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How to escape Tennenbaum's theorem

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arxiv 2209.00967 v1 pith:EDAM2HLL submitted 2022-09-02 math.LO

Fedor Pakhomov This is my paper · ORCID
classification math.LO
keywords theorycomputableconstructdefinitionallyequivalentmodelallowsarithmetic
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We construct a theory definitionally equivalent to first-order Peano arithmetic PA and a non-standard computable model of this theory. The same technique allows us to construct a theory definitionally equivalent to Zermelo-Fraenkel set theory ZF that has a computable model.

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Cited by 2 Pith papers

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  1. Tightness and solidity in fragments of Peano Arithmetic

    math.LO 2025-12 conditional novelty 8.0 of 10

    For every n there is a solid (rigidity-maximal) theory strictly between IΣn and PA, even one that cannot interpret PA; tightness, neatness, and semantic tightness are distinct.

  2. When Bi-interpretability implies Synonymy

    math.LO 2025-06 conditional novelty 8.0 of 10

    For sequential theories, bi-interpretability via one-dimensional identity-preserving interpretations implies synonymy, proved with a weak Schröder-Bernstein theorem; an example shows the hypotheses are optimal.

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