Theory of Completeness for Logical Spaces |
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Authors: | Kensaku Gomi |
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Institution: | 1. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914, Japan
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Abstract: | A logical space is a pair (A, B){(A, {\mathcal{B}})} of a non-empty set A and a subset B{{\mathcal{B}}} of P A{{\mathcal{P}} A} . Since P A{{\mathcal{P}} A} is identified with {0, 1}A and {0, 1} is a typical lattice, a pair (A, F){(A, {\mathcal{F}})} of a non-empty set A and a subset F{{\mathcal{F}}} of
\mathbbBA{{\mathbb{B}}^A} for a certain lattice
\mathbbB{{\mathbb{B}}} is also called a
\mathbbB{{\mathbb{B}}} -valued functional logical space. A deduction system on A is a pair (R, D) of a subset D of A and a relation R between A*
and A. In terms of these simplest concepts, a general framework for studying the logical completeness is constructed. |
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Keywords: | |
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