The nonexistence of unicorns and many-sorted Löwenheim-Skolem theorems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929401757696000 |
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| author | Przybocki, Benjamin Toledo, Guilherme Zohar, Yoni Barrett, Clark |
| author_facet | Przybocki, Benjamin Toledo, Guilherme Zohar, Yoni Barrett, Clark |
| contents | Stable infiniteness, strong finite witnessability, and smoothness are model-theoretic properties relevant to theory combination in satisfiability modulo theories. Theories that are strongly finitely witnessable and smooth are called strongly polite and can be effectively combined with other theories. Toledo, Zohar, and Barrett conjectured that stably infinite and strongly finitely witnessable theories are smooth and therefore strongly polite. They called counterexamples to this conjecture unicorn theories, as their existence seemed unlikely. We prove that, indeed, unicorns do not exist. We also prove versions of the Löwenheim-Skolem theorem and the Łoś-Vaught test for many-sorted logic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18912 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The nonexistence of unicorns and many-sorted Löwenheim-Skolem theorems Przybocki, Benjamin Toledo, Guilherme Zohar, Yoni Barrett, Clark Logic Logic in Computer Science Stable infiniteness, strong finite witnessability, and smoothness are model-theoretic properties relevant to theory combination in satisfiability modulo theories. Theories that are strongly finitely witnessable and smooth are called strongly polite and can be effectively combined with other theories. Toledo, Zohar, and Barrett conjectured that stably infinite and strongly finitely witnessable theories are smooth and therefore strongly polite. They called counterexamples to this conjecture unicorn theories, as their existence seemed unlikely. We prove that, indeed, unicorns do not exist. We also prove versions of the Löwenheim-Skolem theorem and the Łoś-Vaught test for many-sorted logic. |
| title | The nonexistence of unicorns and many-sorted Löwenheim-Skolem theorems |
| topic | Logic Logic in Computer Science |
| url | https://arxiv.org/abs/2406.18912 |