Maximality principles in modal logic and the Axiom of Choice
Fundamenta Mathematicae
MSC: Primary 03E25; Secondary 03B20, 03B44, 03B45, 06D20, 06D22, 06D50, 06E25, 06E15, 18F70
DOI: 10.4064/fm241218-6-5
Published online: 17 October 2025
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 well-known Fine’s and Esakia’s 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).
