Classifying the complexity of models of arithmetic
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913944294129664 |
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| author | Gonzalez, David Łełyk, Mateusz Rossegger, Dino Szlufik, Patryk |
| author_facet | Gonzalez, David Łełyk, Mateusz Rossegger, Dino Szlufik, Patryk |
| contents | We classify the possible Scott complexities for models of Peano arithmetic. We construct models of particular complexities by first giving a complete Scott analysis of colored linear orderings and constructing models of Peano arithmetic from these colored orderings. We also provide tight connections of certain Scott complexities with notions from the classical theory of models of Peano arithmetic, such as prime, finitely generated, and recursively saturated. This effort provides a powerful set of tools to understand the models of Peano arithmetic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12025 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classifying the complexity of models of arithmetic Gonzalez, David Łełyk, Mateusz Rossegger, Dino Szlufik, Patryk Logic 03C62, 03E15, 03H15 We classify the possible Scott complexities for models of Peano arithmetic. We construct models of particular complexities by first giving a complete Scott analysis of colored linear orderings and constructing models of Peano arithmetic from these colored orderings. We also provide tight connections of certain Scott complexities with notions from the classical theory of models of Peano arithmetic, such as prime, finitely generated, and recursively saturated. This effort provides a powerful set of tools to understand the models of Peano arithmetic. |
| title | Classifying the complexity of models of arithmetic |
| topic | Logic 03C62, 03E15, 03H15 |
| url | https://arxiv.org/abs/2507.12025 |