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Sets, models and proofs

Moerdijk, Ieke.

Sets, models and proofs

Record Type:	Electronic resources : Monograph/item
Title/Author:	Sets, models and proofsby Ieke Moerdijk, Jaap van Oosten.
Author:	Moerdijk, Ieke.
other author:	Oosten, Jaap van.
Published:	Cham :Springer International Publishing :2018.
Description:	xiv, 141 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Logic, Symbolic and mathematical.
Online resource:	https://doi.org/10.1007/978-3-319-92414-4
ISBN:	9783319924144$q(electronic bk.)

Sets, models and proofs
Moerdijk, Ieke.

Sets, models and proofs[electronic resource] /by Ieke Moerdijk, Jaap van Oosten. - Cham :Springer International Publishing :2018. - xiv, 141 p. :ill., digital ;24 cm. - Springer undergraduate mathematics series,1615-2085. - Springer undergraduate mathematics series..

Introduction -- 1 Sets -- 2 Models -- 3 Proofs -- 4 Sets Again -- Appendix: Topics for Further Study -- Photo Credits -- Bibliography -- Index.

This textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas. The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzen-style natural deduction and a detailed proof of Godel's completeness theorem for first-order logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for self-study, though it is ideally suited as a text for a one-semester university course in the second or third year.

ISBN: 9783319924144$q(electronic bk.)

Standard No.: 10.1007/978-3-319-92414-4doiSubjects--Topical Terms:

180452
Logic, Symbolic and mathematical.

LC Class. No.: QA9 / .M647 2018

Dewey Class. No.: 511.3

Sets, models and proofs
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300 $a xiv, 141 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer undergraduate mathematics series, $x 1615-2085
505 0 $a Introduction -- 1 Sets -- 2 Models -- 3 Proofs -- 4 Sets Again -- Appendix: Topics for Further Study -- Photo Credits -- Bibliography -- Index.
520 $a This textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas. The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzen-style natural deduction and a detailed proof of Godel's completeness theorem for first-order logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for self-study, though it is ideally suited as a text for a one-semester university course in the second or third year.
650 0 $a Logic, Symbolic and mathematical. $3 180452
650 1 4 $a Structures and Proofs. $3 826604
650 2 4 $a Algebra. $3 188312
700 1 $a Oosten, Jaap van. $3 455104
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950 $a Mathematics and Statistics (Springer-11649)