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Generic substitutions

Published online by Cambridge University Press:  12 March 2014

Giovanni Panti
Giovanni Panti*
Affiliation:
Department of Mathematics, University of Udine, Via Delle Scienze 208, 33100 Udine, Italy, E-mail: panti@dimi.uniud.it
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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.

Keywords

algebraic logicsubstitutionstochastic propertiesspectral spaces
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 1 , March 2005 , pp. 61 - 83
Copyright
Copyright © Association for Symbolic Logic 2005

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