] > Tennenbaum's Theorem for Models of Arithmetic

Tennenbaum's Theorem for Models of Arithmetic

Abstract

This paper discusses Tennenbaum's Theorem in its original context of models of arithmetic, which states that there are no recursive nonstandard models of Peano Arithmetic. We focus on three separate areas: the historical background to the theorem; an understanding of the theorem and its relationship with the Gödel–Rosser Theorem; and extensions of Tennenbaum's theorem to diophantine problems in models of arthmetic, especially problems concerning which diophantine equations have roots in some model of a given theory of arithmetic.

Tennenbaum's Theorem: some historical background

Tennenbaum's Theorem

Tennenbaum's Theorem and diophantine problems

References

Author: Richard Kaye, School of Mathematics, University of Birmingham