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Fregean subtractive varieties with definable congruence

Published online by Cambridge University Press:  09 April 2009

Paolo Agliano
Affiliation:
Dipartimento di Matematica, Via del Capitano 15, 53100, Siena, Italy e-mail: agliano@unisi.it
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Abstract

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In this paper we investigate subtractive varieties of algebras that are Fregean in order to get structure theorems about them. For instance it turns out that a subtractive variety is Fregean and has equationally definable principal congruences if and only if it is termwise equivalent to a variety of Hilbert algebras with compatible operations. Several examples are provided to illustrate the theory.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2001

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