Maximality Principles in Modal Logic and the Axiom of Choice

Rodrigo Nicolau Almeida; Guram Bezhanishvili

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arXiv · 2412.13706

Maximality Principles in Modal Logic and the Axiom of Choice

Rodrigo Nicolau Almeida·Guram Bezhanishvili

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Abstract

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).

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BibTeX RIS

Rodrigo Nicolau Almeida, Guram Bezhanishvili. 2024-12-18. Maximality Principles in Modal Logic and the Axiom of Choice. https://arxiv.org/abs/2412.13706

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