Format:
1 Online-Ressource (xii, 204 pages)
,
digital, PDF file(s)
ISBN:
9780511619243
Content:
This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with König's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis
Content:
König's lemma -- Posets and maximal elements -- Formal systems -- Deductions in posets -- Boolean algebras -- Propositional logic -- Valuations -- Filters and ideals -- First-order logic -- Completeness and compactness -- Model theory -- Nonstandard analysis
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Additional Edition:
ISBN 9780521882194
Additional Edition:
ISBN 9780521708777
Additional Edition:
Print version ISBN 9780521882194
Language:
English
DOI:
10.1017/CBO9780511619243
URL:
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