Description |
1 online resource (v, 78 pages) : illustrations |
Series |
Memoirs of the American Mathematical Society, 1947-6221 ; v. 396 |
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Memoirs of the American Mathematical Society ; no. 396. 0065-9266
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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.
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31.10 logic, set theory.
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MATHEMATICS -- Essays.
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MATHEMATICS -- Pre-Calculus.
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MATHEMATICS -- Reference.
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Algebraic logic
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Algebraisierbare Logik
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Mathematische Logik
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Algebraïsche logica.
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Logica Matematica.
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Form |
Electronic book
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Author |
Pigozzi, Don, 1935-
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ISBN |
9781470408169 |
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1470408163 |
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