English

A theory satisfying a strong version of Tennenbaum's theorem

Logic 2023-09-22 v1

Abstract

We answer a question of Pakhomov by showing that there is a consistent, c.e. theory TT such that no theory which is definitionally equivalent to TT has a computable model. A key tool in our proof is the model-theoretic notion of mutual algebraicity.

Keywords

Cite

@article{arxiv.2309.11598,
  title  = {A theory satisfying a strong version of Tennenbaum's theorem},
  author = {Patrick Lutz and James Walsh},
  journal= {arXiv preprint arXiv:2309.11598},
  year   = {2023}
}

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21 pages