國立虎尾科技大學 |

Sets, Models and Proofs

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Sets, Models and Proofs/ by Ieke Moerdijk, Jaap van Oosten.
Author:	Moerdijk, Ieke.
other author:	van Oosten, Jaap.
Description:	XIV, 141 p. 39 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Proof theory. -
Online resource:	https://doi.org/10.1007/978-3-319-92414-4
ISBN:	9783319924144

Sets, Models and Proofs
Moerdijk, Ieke.

Sets, Models and Proofs[electronic resource] /by Ieke Moerdijk, Jaap van Oosten. - 1st ed. 2018. - XIV, 141 p. 39 illus.online resource. - 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 Gödel’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

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

579943
Proof theory.

LC Class. No.: QA9.54

Dewey Class. No.: 511.3

Sets, Models and Proofs
LDR:02674nam a22003975i 4500 001 988157
003 DE-He213
005 20200703073641.0
007 cr nn 008mamaa
008 201225s2018 gw | s |||| 0|eng d
020 $a 9783319924144 $9 978-3-319-92414-4
024 7 $a 10.1007/978-3-319-92414-4 $2 doi
035 $a 978-3-319-92414-4
050 4 $a QA9.54
072 7 $a PBCD $2 bicssc
072 7 $a MAT018000 $2 bisacsh
072 7 $a PBCD $2 thema
082 0 4 $a 511.3 $2 23
100 1 $a Moerdijk, Ieke. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1211325
245 1 0 $a Sets, Models and Proofs $h [electronic resource] / $c by Ieke Moerdijk, Jaap van Oosten.
250 $a 1st ed. 2018.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a XIV, 141 p. 39 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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 Gödel’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 Proof theory. $3 579943
650 0 $a Algebra. $2 gtt $3 579870
650 1 4 $a Structures and Proofs. $3 1211326
700 1 $a van Oosten, Jaap. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1280473
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319924137
776 0 8 $i Printed edition: $z 9783319924151
830 0 $a Springer Undergraduate Mathematics Series, $x 1615-2085 $3 1255356
856 4 0 $u https://doi.org/10.1007/978-3-319-92414-4
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)