How to escape Tennenbaum's theorem

2022/09/02 by Pakhomov, Fedor · 3 citations
#03C57 #03C62 #F.4.1 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2209.00967

Abstract

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.

Cited by

• Tightness and solidity in fragments of Peano Arithmetic
• ESCAPING TENNENBAUM’S THEOREM AND A STRONG JUMP INVERSION THEOREM
• When Bi-interpretability implies Synonymy

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