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Books > Science & Mathematics > Mathematics > Algebra
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Set Theoretical Logic-The Algebra of Models (Hardcover)
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Set Theoretical Logic-The Algebra of Models (Hardcover)
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An introduction to mathematical logic covering all the usual
topics: compactness and axiomatizability of semantical consequence;
Lowenheim-Skolem-Tarski theorems; prenex and other normal forms;
and characterizations of elementary classes with help of
ultraproducts. Logic is based exclusively on semantics. Truth and
satisfiability of formulas in structures are the basic notions, and
there is no need to mention logical calculi with axioms and rules
(they are the subjects of Volume Two). The methods are algebraic in
the sense that notions such as homomorphisms and congruence
relations are applied throughout, and this not just as
abbreviations, but in order to gain new insights. These concepts
are developed in an introductory chapter which, together with
chapters five to nine on equations, can be viewed as a first course
on universal algebra. The approach to algorithms generating
semantical consequences is algebraic as well: for equations in
algebras, for propositional formulas, for open formulas of
predicate logic, and for the formulas of quantifier logic. The
structural description of logical consequence is a straightforward
extension of that of equational consequence as long as Bool
General
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