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Record Nr. |
UNINA9910624311203321 |
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Autore |
Andréka H. |
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Titolo |
Universal algebraic logic : dedicated to the unity of science / / Hajnal Andréka, [and three others] |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2022] |
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©2022 |
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ISBN |
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Descrizione fisica |
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1 online resource (337 pages) |
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Collana |
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Studies in Universal Logic |
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Disciplina |
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Soggetti |
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Algebraic logic |
Lògica algebraica |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Intro -- Preface -- Acknowledgement -- Contents -- Chapter 1 Notation, Elementary Concepts -- 1.1 Sets, classes, tuples, simple operations on sets -- 1.2 Binary relations, equivalence relations, functions -- 1.3 Orderings, ordinals, cardinals -- 1.4 Sequences -- 1.5 Direct product of families of sets -- 1.6 Relations of higher ranks -- 1.7 Closure systems -- 1.8 First{order logic (FOL) -- Chapter 2 Basics from Universal Algebra -- 2.1 Examples for algebras -- 2.2 Building new algebras from old ones (operations on algebras) -- 2.2.1 Subalgebra -- 2.2.2 Homomorphic image -- 2.2.3 A distinguished example: Lattices -- 2.2.4 Congruence relation -- 2.2.5 Cartesian product, direct decomposition -- 2.2.6 Subdirect decomposition -- 2.2.7 Ultraproduct, reduced product -- 2.3 Categories -- 2.4 Variety characterization, quasi{variety characterization -- 2.5 Free algebras -- 2.6 Boolean Algebras -- 2.7 Discriminator varieties -- 2.8 Boolean Ordered Algebras (Boas), Boolean Algebras with Operators (BAOs) -- Chapter 3 General framework and algebraization -- 3.1 De ning the framework for studying logics -- 3.2 Concrete logics in the new framework -- 3.3 Algebraization -- 3.3.1 Having connectives, formula algebra -- 3.3.2 Compositionality, tautological formula algebra -- 3.3.3 Algebraic counterparts of a logic -- 3.3.4 Substitution properties -- 3.3.5 Filter property -- 3.3.6 General Logics -- 3.4 Connections |
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with Abstract Algebraic Logic, Abstract Model Theory and Institutions -- Chapter 4 Bridge between logic and algebra -- 4.1 Algebraic characterization of compactness properties -- 4.2 Algebraic characterizations of completeness properties -- 4.2.1 Hilbert-type inference systems -- 4.2.2 Completeness and soundness -- 4.3 Algebraic characterization of definability properties -- 4.3.1 Syntactical Beth definability property -- 4.3.2 Beth definability property. |
4.3.3 Local Beth definability property -- 4.3.4 Weak Beth definability property -- 4.4 Algebraic characterization of interpolation properties -- 4.4.1 Interpolation properties -- 4.4.2 Amalgamation and interpolation properties -- 4.5 Decidability -- 4.6 Gödel's incompleteness property -- Chapter 5 Applying the machinery: Examples -- 5.1 Classical propositional logic LC -- 5.2 Arrow logic LREL -- 5.3 Finite-variable fragments of first-order logic, with substituted atomic formulas, L'n -- 5.4 n-variable fragment Ln of first-order logic, for n ≤ ω -- 5.5 First-order logic with nonstandard semantics, Lan -- 5.6 Variable-dependent rst-order logic, Lnvd -- 5.7 First-order logic, ranked version, LFOLranked -- 5.8 First-order logic, rank-free (or type-less) version, LFOLrf -- Chapter 6 Generalizations and new kinds of logics -- 6.1 Generalizations -- 6.2 New kinds of logics -- Chapter 7 Appendix: Algebras of relations -- 7.1 Algebras of binary relations -- 7.2 Algebras of finitary relations -- 7.3 All finitary relations together -- Bibliography -- Index -- Index of symbols. |
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