Set Theoretical Logic-The Algebra of Models W. Felscher

ISBN: 9789056992668

Published: May 30th 2000

Hardcover

296 pages


Description

Set Theoretical Logic-The Algebra of Models  by  W. Felscher

Set Theoretical Logic-The Algebra of Models by W. Felscher
May 30th 2000 | Hardcover | PDF, EPUB, FB2, DjVu, AUDIO, mp3, RTF | 296 pages | ISBN: 9789056992668 | 10.66 Mb

This is an introduction to mathematical logic in which all the usual topics are presented: compactness and axiomatizability of semantical consequence, Lowenheim-Skolem-Tarski theorems, prenex and other normal forms, and characterizations ofMoreThis is an introduction to mathematical logic in which all the usual topics are presented: compactness and axiomatizability of semantical consequence, Lowenheim-Skolem-Tarski theorems, prenex and other normal forms, and characterizations of elementary classes with the help of ultraproducts.

Logic is based exclusively on semantics: truth and satisfiability of formulas in structures are the basic notions. The methods are algebraic in the sense that notions such as homomorphisms and congruence relations are applied throughout in order to gain new insights. These concepts are developed and 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 Boolean valued propositions and Boolean valued structures are considered- the reduction of the classical 2-valued case then depends on the Boolean prime ideal theorem.



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