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Finitely generated free Heyting algebras via Birkhoff duality and coalgebra

Nick Bezhanishvili ; Mai Gehrke.

Algebras axiomatized entirely by rank 1 axioms are algebras for a functor and thus the free algebras can be obtained by a direct limit process. Dually, the final coalgebras can be obtained by an inverse limit process. In order to explore the limits of this method we look at Heyting algebras which&nbsp;[&hellip;]

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A Coalgebraic Approach to Dualities for Neighborhood Frames

Guram Bezhanishvili ; Nick Bezhanishvili ; Jim de Groot.

We develop a uniform coalgebraic approach to J\'onsson-Tarski and Thomason type dualities for various classes of neighborhood frames and neighborhood algebras. In the first part of the paper we construct an endofunctor on the category of complete and atomic Boolean algebras that is dual to the&nbsp;[&hellip;]

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Geometric Model Checking of Continuous Space

Nick Bezhanishvili ; Vincenzo Ciancia ; David Gabelaia ; Gianluca Grilletti ; Diego Latella ; Mieke Massink.

Topological Spatial Model Checking is a recent paradigm where model checking techniques are developed for the topological interpretation of Modal Logic. The Spatial Logic of Closure Spaces, SLCS, extends Modal Logic with reachability connectives that, in turn, can be used for expressing interesting&nbsp;[&hellip;]

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Coalgebraic Geometric Logic: Basic Theory

Nick Bezhanishvili ; Jim de Groot ; Yde Venema.

Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebras for an endofunctor on some full subcategory of the category of topological spaces and continuous functions. We&nbsp;[&hellip;]

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