Modal Measurable Logics via a Modal Loomis-Sikorski Representation Theorem

Nick Bezhanishvili; Jim de Groot; Lawrence S. Moss

doi:10.4204/eptcs.447.9

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arXiv · 2606.31862

Modal Measurable Logics via a Modal Loomis-Sikorski Representation Theorem

Nick Bezhanishvili·Jim de Groot·Lawrence S. Moss

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Abstract

We investigate a modal extension of the infinitary classical logic with countable meets and joins, formulated with an eye toward measure-theoretic work in dynamical systems and in point-free ergodic theory. We define a modal formalism in this language, which we call modal measurable logics. We also introduce a Kripke-like semantics for these logics in measurable spaces taking a designated modal sigma-ideal into consideration. Using a restriction of Jonsson-Tarski duality and a modal extension of the Loomis-Sikorski theorem, we prove completeness of modal measurable logics with respect to this new semantics.

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BibTeX RIS

Nick Bezhanishvili, Jim de Groot, Lawrence S. Moss. 2026-06-30. Modal Measurable Logics via a Modal Loomis-Sikorski Representation Theorem. https://doi.org/10.4204/eptcs.447.9

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