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The mathematics of logic : = a guide to completeness theorems and their applications /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The mathematics of logic :/ Richard Kaye.
其他題名:	a guide to completeness theorems and their applications /
作者:	Kaye, Richard
面頁冊數:	1 online resource (xii, 204 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Logic, Symbolic and mathematical. -
電子資源:	https://doi.org/10.1017/CBO9780511619243
ISBN:	9780511619243 (ebook)

The mathematics of logic : = a guide to completeness theorems and their applications /
Kaye, Richard

The mathematics of logic :a guide to completeness theorems and their applications /Richard Kaye. - 1 online resource (xii, 204 pages) :digital, PDF file(s).

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

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.

ISBN: 9780511619243 (ebook)Subjects--Topical Terms:

527823
Logic, Symbolic and mathematical.

LC Class. No.: QA9 / .K32 2007

Dewey Class. No.: 511.3

The mathematics of logic : = a guide to completeness theorems and their applications /
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a 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.
520 $a 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.
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856 4 0 $u https://doi.org/10.1017/CBO9780511619243