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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2509.15191 |
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| _version_ | 1866914046205231104 |
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| author | Murwanashyaka, Juvenal |
| author_facet | Murwanashyaka, Juvenal |
| contents | Albert Visser has shown that Robinson's $ \mathsf{Q} $ and Gregorczyk's $ \mathsf{TC} $ are not sequential by showing that these theories are not even poly-pair theories, which, in a strong sense, means these theories lack pairing. In this paper, we use Ehrenfeucht-Fraïssé games to show that the theory $ \mathsf{Q} + Θ$ we obtain by extending Robinson's $ \mathsf{Q} $ with an axiom $ Θ$ which says that the map $ π(x, y ) = (x+y)^2 + x $ is a pairing function is not sequential; in fact, we show that this theory is not even a Vaught theory. As a corollary, we get that the tree theory $ \mathsf{T} $ of [Kristiansen & Murwanashyaka, 2020] is also not a Vaught theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15191 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A non-sequential arithmetical theory with pairing Murwanashyaka, Juvenal Logic Albert Visser has shown that Robinson's $ \mathsf{Q} $ and Gregorczyk's $ \mathsf{TC} $ are not sequential by showing that these theories are not even poly-pair theories, which, in a strong sense, means these theories lack pairing. In this paper, we use Ehrenfeucht-Fraïssé games to show that the theory $ \mathsf{Q} + Θ$ we obtain by extending Robinson's $ \mathsf{Q} $ with an axiom $ Θ$ which says that the map $ π(x, y ) = (x+y)^2 + x $ is a pairing function is not sequential; in fact, we show that this theory is not even a Vaught theory. As a corollary, we get that the tree theory $ \mathsf{T} $ of [Kristiansen & Murwanashyaka, 2020] is also not a Vaught theory. |
| title | A non-sequential arithmetical theory with pairing |
| topic | Logic |
| url | https://arxiv.org/abs/2509.15191 |