Algebraizable logics

by Blok, W. J.

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Title Statements

Full title :Algebraizable logics / W.J. Blok and Don Pigozzi.

Summary

The main result of the paper is an intrinsic characterization of algebraizability in terms of the Leibniz operator [capital Greek]Omega, which associates with each theory [italic]T of a given deductive system [script]S a congruence relation [capital Greek]Omega[italic]T on the formula algebra. [capital Greek]Omega[italic]T identifies all formulas that cannot be distinguished from one another, on the basis of [italic]T, by any property expressible in the language of [script]S. The characterization theorem states that a deductive system [script]S is algebraizable if and only if [capital Greek]Omega is one-to-one and order-preserving on the lattice of [script]S-theories, and in addition preserves directed unions. Several other characteristics are given. The results and concepts are illustrated by a large number of examples from modal and intuitionistic logic, relevance logic, and classical predicate logic.

Edition Statements

Publication Date:©1989.

Publication Statements

Publisher(s):American mathematical Society
Place of Publication:Providence, R.I., USA
Language:eng
Publication Date:©1989.

Notes

"Volume 77, number 396 (third of 4 numbers)."

The Physical Object

Description:v, 78 pages : : illustrations ; : 26 cm.

Edition Identifiers

ISBN:0821824597, 9780821824597
oclc:ocm18463954
LC Classification:QA3
Dewey Decimal:510 s

Subjects

31.10 logic, set theory Algebraic logic Algebraïsche logica Algebraisierbare Logik Logic, Symbolic and mathematical Lógica matemática Logique algébrique Logique symbolique et mathématique Mathematische Logik