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March 2005 Generic substitutions
Giovanni Panti
J. Symbolic Logic 70(1): 61-83 (March 2005). DOI: 10.2178/jsl/1107298510

Abstract

Up to equivalence, a substitution in propositional logic is an endomorphism of its free algebra. On the dual space, this results in a continuous function, and whenever the space carries a natural measure one may ask about the stochastic properties of the action. In classical logic there is a strong dichotomy: while over finitely many propositional variables everything is trivial, the study of the continuous transformations of the Cantor space is the subject of an extensive literature, and is far from being a completed task. In many-valued logic this dichotomy disappears: already in the finite-variable case many interesting phenomena occur, and the present paper aims at displaying some of these.

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Giovanni Panti. "Generic substitutions." J. Symbolic Logic 70 (1) 61 - 83, March 2005. https://doi.org/10.2178/jsl/1107298510

Information

Published: March 2005
First available in Project Euclid: 1 February 2005

zbMATH: 1089.03017
MathSciNet: MR2119123
Digital Object Identifier: 10.2178/jsl/1107298510

Subjects:
Primary: 03B50 , ‎37B05‎

Keywords: algebraic logic , spectral spaces , stochastic properties , substitution

Rights: Copyright © 2005 Association for Symbolic Logic

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Vol.70 • No. 1 • March 2005
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