Maximality Principles in Modal Logic and the Axiom of Choice
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912160653770752 |
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| author | Almeida, Rodrigo Nicolau Bezhanishvili, Guram |
| author_facet | Almeida, Rodrigo Nicolau Bezhanishvili, Guram |
| contents | We investigate the set-theoretic strength of several maximality principles that play an important role in the study of modal and intuitionistic logics. We focus on the well-known Fine and Esakia maximality principles, present two formulations of each, and show that the stronger formulations are equivalent to the Axiom of Choice (AC), while the weaker ones to the Boolean Prime Ideal Theorem (BPI). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13706 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximality Principles in Modal Logic and the Axiom of Choice Almeida, Rodrigo Nicolau Bezhanishvili, Guram Logic 03E25, 03B20, 03B44, 03B45, 06D20, 06D22, 06D50, 06E25, 06E15, 18F70 We investigate the set-theoretic strength of several maximality principles that play an important role in the study of modal and intuitionistic logics. We focus on the well-known Fine and Esakia maximality principles, present two formulations of each, and show that the stronger formulations are equivalent to the Axiom of Choice (AC), while the weaker ones to the Boolean Prime Ideal Theorem (BPI). |
| title | Maximality Principles in Modal Logic and the Axiom of Choice |
| topic | Logic 03E25, 03B20, 03B44, 03B45, 06D20, 06D22, 06D50, 06E25, 06E15, 18F70 |
| url | https://arxiv.org/abs/2412.13706 |