A Topological Tennenbaum Theorem
We prove that in Borel models of arithmetic on an uncountable Polish space, neither addition nor multiplication is continuous. This is an analogue of Tennenbaum's Theorem for topological models of arithmetic. This answers a question of Enayat, Hamkins, and Wcis{\l}o.
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | We prove that in Borel models of arithmetic on an uncountable Polish space,
neither addition nor multiplication is continuous. This is an analogue of
Tennenbaum's Theorem for topological models of arithmetic. This answers a
question of Enayat, Hamkins, and Wcis{\l}o. |
|---|---|
| DOI: | 10.48550/arxiv.2311.13699 |