The Borel complexity of the class of models of first-order theories
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916651997331456 |
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| author | Andrews, Uri Gonzalez, David Lempp, Steffen Rossegger, Dino Zhu, Hongyu |
| author_facet | Andrews, Uri Gonzalez, David Lempp, Steffen Rossegger, Dino Zhu, Hongyu |
| contents | We investigate the descriptive complexity of the set of models of first-order theories. Using classical results of Knight and Solovay, we give a sharp condition for complete theories to have a $\pmbΠ_ω^0$-complete set of models. In particular, any sequential theory (a class of foundational theories isolated by Pudlák) has a $\pmbΠ_ω^0$-complete set of models. We also give sharp conditions for theories to have a $\pmbΠ^0_n$-complete set of models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10029 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Borel complexity of the class of models of first-order theories Andrews, Uri Gonzalez, David Lempp, Steffen Rossegger, Dino Zhu, Hongyu Logic 03C62, 03C52, 03E15 We investigate the descriptive complexity of the set of models of first-order theories. Using classical results of Knight and Solovay, we give a sharp condition for complete theories to have a $\pmbΠ_ω^0$-complete set of models. In particular, any sequential theory (a class of foundational theories isolated by Pudlák) has a $\pmbΠ_ω^0$-complete set of models. We also give sharp conditions for theories to have a $\pmbΠ^0_n$-complete set of models. |
| title | The Borel complexity of the class of models of first-order theories |
| topic | Logic 03C62, 03C52, 03E15 |
| url | https://arxiv.org/abs/2402.10029 |