Taking inspiration from the monadicity of complete atomic Boolean algebras, we prove that profinite modal algebras are monadic over Set. While analyzing the monadic functor, we recover the universal model construction - a construction widely used in the modal logic literature for describing finitely generated free modal algebras and the essentially finite generated subframes of their canonical models. (c) 2024 Elsevier B.V. All rights reserved.
Profiniteness, monadicity and universal models in modal logic / M. De Berardinis, S. Ghilardi. - In: ANNALS OF PURE AND APPLIED LOGIC. - ISSN 0168-0072. - 175:7(2024), pp. 103454.1-103454.25. [10.1016/j.apal.2024.103454]
Profiniteness, monadicity and universal models in modal logic
S. Ghilardi
Ultimo
2024
Abstract
Taking inspiration from the monadicity of complete atomic Boolean algebras, we prove that profinite modal algebras are monadic over Set. While analyzing the monadic functor, we recover the universal model construction - a construction widely used in the modal logic literature for describing finitely generated free modal algebras and the essentially finite generated subframes of their canonical models. (c) 2024 Elsevier B.V. All rights reserved.
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