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Preface -- Acknowledgement -- 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) -- 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 Boas and BAOs -- 3 General framework and algebraization -- 3.1 Defining 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 with Abstract Algebraic Logic, Abstract Model Theory and Institutions -- 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 Godel's incompleteness property -- 5 Applying the machinery: Examples -- 5.1 Classical propositional logic LC -- 5.2 Arrow logic L_{REL} -- 5.3 Finite-variable fragments of first-order logic, with substituted atomic formulas, L'_n -- 5.4 n-variable fragment L_n of rst-order logic, for n \le \omega -- 5.5 First-order logic with nonstandard semantics, L^{a}_{n} -- 5.6 Variable-dependent first-order logic, L^{vd}_{n} -- 5.7 First-order logic, ranked version, L^{ranked}_{FOL} -- 5.8 First-order logic, rank-free (or type-less) version, L^{rf}_{FOL} -- 6 Generalizations and new kinds of logics -- 6.1 Generalizations -- 6.2 New kinds of logics -- 7 Appendix: Algebras of relations -- 7.1 Algebras of binary relations -- 7.2 Algebras of unitary relations -- 7.3 All unitary relations together -- Bibliography -- Index -- Index of symbols.
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