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A topological approach to the compactness of many-valued propositional logic and first-order logic
By Lirong Xia and Mingsheng Ying.
In Preparation.
Abstract
Compactness is one of the most important properties
in logic. In this paper, we approach the compactness in many-valued
propositional logic and first order logic from a semantic and
topological perspective. Without utilizing completeness, we show
than under certain topology, the topological spaces of all models of
such logics are compact. Our approach thus build a bridge between
the compactness in logic and topological space. Therefore it can be
used to analyze the compactness of logics, especially when no
completeness result is proved.
Paper
Available upon request.