Representations of bounded distributive lattices as the continuous sections of Sheaves based on the Priestly and Zarski topologies

Tarek Sayed Ahmed

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arXiv · 1304.0612

Representations of bounded distributive lattices as the continuous sections of Sheaves based on the Priestly and Zarski topologies

Tarek Sayed Ahmed

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Abstract

Using Sheaf duality theory of Comer for cylindric algebras, we give a representation theorem of of distributive bounded lattices expanded by modalities (functions distributing over joins) as the continuous sections of sheaves. Our representation is defined via a contravariant functor. We give applications to many-valued logics logics and various modifications of first order logic and multi-modal logic, set in an algebraic framework.

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BibTeX RIS

Tarek Sayed Ahmed. 2013-04-02. Representations of bounded distributive lattices as the continuous sections of Sheaves based on the Priestly and Zarski topologies. https://arxiv.org/abs/1304.0612

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