# Theory of Completeness for Logical Spaces

@article{Gomi2009TheoryOC,
title={Theory of Completeness for Logical Spaces},
author={Kensaku Gomi},
journal={Logica Universalis},
year={2009},
volume={3},
pages={243-291}
}
• Kensaku Gomi
• Published 6 August 2009
• Mathematics, Philosophy
• Logica Universalis
A logical space is a pair $${(A, {\mathcal{B}})}$$ of a non-empty set A and a subset $${{\mathcal{B}}}$$ of $${{\mathcal{P}} A}$$ . Since $${{\mathcal{P}} A}$$ is identified with {0, 1}A and {0, 1} is a typical lattice, a pair $${(A, {\mathcal{F}})}$$ of a non-empty set A and a subset $${{\mathcal{F}}}$$ of $${{\mathbb{B}}^A}$$ for a certain lattice $${{\mathbb{B}}}$$ is also called a $${{\mathbb{B}}}$$ -valued functional logical space. A deduction system on A is a pair (R, D) of a subset D of…
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