The <Tennenbaum theorem> states that no countable nonstandard model of <Peano arithmetic> has a presentation on $\mathbb N$ in which both its addition and multiplication operations are recursive.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 120 / 3 / e / Solution

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Tennenbaum's theorem says that no countable nonstandard model of <Peano arithmetic> can have both addition and multiplication computable under a presentation of its domain by the natural numbers.

Tennenbaum theorem

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Peano arithmetic is the first-order theory of the natural numbers with zero, successor, addition, multiplication, order, and the induction scheme.


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