Maximality Principles in Modal Logic and the Axiom of Choice

Fuente: arXiv
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Main Authors: Almeida, Rodrigo Nicolau, Bezhanishvili, Guram
Format: Preprint
Published: 2024
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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