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Summer 1998 Homeomorphism and the Equivalence of Logical Systems
Stephen Pollard
Notre Dame J. Formal Logic 39(3): 422-435 (Summer 1998). DOI: 10.1305/ndjfl/1039182255

Abstract

Say that a property is topological if and only if it is invariant under homeomorphism. Homeomorphism would be a successful criterion for the equivalence of logical systems only if every logically significant property of every logical system were topological. Alas, homeomorphisms are sometimes insensitive to distinctions that logicians value: properties such as functional completeness are not topological. So logics are not just devices for exploring closure topologies. One still wonders, though, how much of logic is topological. This essay examines some logically significant properties that are topological (or are topological in some important class). In the process, we learn something about the conditions under which the meaning of a connective can be "given by the connective's role in inference."

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Stephen Pollard. "Homeomorphism and the Equivalence of Logical Systems." Notre Dame J. Formal Logic 39 (3) 422 - 435, Summer 1998. https://doi.org/10.1305/ndjfl/1039182255

Information

Published: Summer 1998
First available in Project Euclid: 6 December 2002

zbMATH: 0967.03007
MathSciNet: MR1741547
Digital Object Identifier: 10.1305/ndjfl/1039182255

Subjects:
Primary: 03B22
Secondary: 03B30 , 03G99

Rights: Copyright © 1998 University of Notre Dame

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Vol.39 • No. 3 • Summer 1998
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