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Book Cover
E-book
Author Blok, W. J., 1947-

Title Algebraizable logics / W.J. Blok and Don Pigozzi
Published Providence, R.I., USA : American Mathematical Society, ©1989

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Description 1 online resource (v, 78 pages) : illustrations
Series Memoirs of the American Mathematical Society, 1947-6221 ; v. 396
Memoirs of the American Mathematical Society ; no. 396. 0065-9266
Contents Introduction 1. Deductive systems and matrix semantics 2. Equational consequence and algebraic semantics 3. The lattice of theories 4. Two intrinsic characterizations 5. Matrix semantics and algebraizability Appendix A. Elementary definitional equivalence Appendix B. An example Appendix C. Predicate logic
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
Analysis Algebraic logic
Notes "Volume 77, number 396 (third of 4 numbers)."
Bibliography Includes bibliographical references (pages 73-76) and index
Notes Print version record
Subject Algebraic logic.
31.10 logic, set theory.
MATHEMATICS -- Essays.
MATHEMATICS -- Pre-Calculus.
MATHEMATICS -- Reference.
Algebraic logic
Algebraisierbare Logik
Mathematische Logik
Algebraïsche logica.
Logica Matematica.
Form Electronic book
Author Pigozzi, Don, 1935-
ISBN 9781470408169
1470408163