東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Mathematical logic

Ebbinghaus, Heinz-Dieter.

Linked to FindBook

Google Book

Amazon

博客來

Mathematical logic

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mathematical logic/ by Heinz-Dieter Ebbinghaus, Jorg Flum, Wolfgang Thomas.
Author:	Ebbinghaus, Heinz-Dieter.
other author:	Flum, Jorg.
Published:	Cham :Springer International Publishing : : 2021.,
Description:	ix, 304 p. :ill., digital ;24 cm.
[NT 15003449]:	A -- I Introduction -- II Syntax of First-Order Languages -- III Semantics of First-Order Languages -- IV A Sequent Calculus -- V The Completeness Theorem -- VI The Lowenheim-Skolem and the Compactness Theorem -- VII The Scope of First-Order Logic -- VIII Syntactic Interpretations and Normal Forms -- B -- IX Extensions of First-Order Logic -- X Computability and Its Limitations -- XI Free Models and Logic Programming -- XII An Algebraic Characterization of Elementary Equivalence -- XIII Lindstrom's Theorems -- References -- List of Symbols -- Subject Index.
Contained By:	Springer Nature eBook
Subject:	Logic, Symbolic and mathematical. -
Online resource:	https://doi.org/10.1007/978-3-030-73839-6
ISBN:	9783030738396

Mathematical logic
Ebbinghaus, Heinz-Dieter.

Mathematical logic[electronic resource] /by Heinz-Dieter Ebbinghaus, Jorg Flum, Wolfgang Thomas. - Third edition. - Cham :Springer International Publishing :2021. - ix, 304 p. :ill., digital ;24 cm. - Graduate texts in mathematics,2910072-5285 ;. - Graduate texts in mathematics ;291..

A -- I Introduction -- II Syntax of First-Order Languages -- III Semantics of First-Order Languages -- IV A Sequent Calculus -- V The Completeness Theorem -- VI The Lowenheim-Skolem and the Compactness Theorem -- VII The Scope of First-Order Logic -- VIII Syntactic Interpretations and Normal Forms -- B -- IX Extensions of First-Order Logic -- X Computability and Its Limitations -- XI Free Models and Logic Programming -- XII An Algebraic Characterization of Elementary Equivalence -- XIII Lindstrom's Theorems -- References -- List of Symbols -- Subject Index.

This textbook introduces first-order logic and its role in the foundations of mathematics by examining fundamental questions. What is a mathematical proof? How can mathematical proofs be justified? Are there limitations to provability? To what extent can machines carry out mathematical proofs? In answering these questions, this textbook explores the capabilities and limitations of algorithms and proof methods in mathematics and computer science. The chapters are carefully organized, featuring complete proofs and numerous examples throughout. Beginning with motivating examples, the book goes on to present the syntax and semantics of first-order logic. After providing a sequent calculus for this logic, a Henkin-type proof of the completeness theorem is given. These introductory chapters prepare the reader for the advanced topics that follow, such as Godel's Incompleteness Theorems, Trakhtenbrot's undecidability theorem, Lindstrom's theorems on the maximality of first-order logic, and results linking logic with automata theory. This new edition features many modernizations, as well as two additional important results: The decidability of Presburger arithmetic, and the decidability of the weak monadic theory of the successor function. Mathematical Logic is ideal for students beginning their studies in logic and the foundations of mathematics. Although the primary audience for this textbook will be graduate students or advanced undergraduates in mathematics or computer science, in fact the book has few formal prerequisites. It demands of the reader only mathematical maturity and experience with basic abstract structures, such as those encountered in discrete mathematics or algebra.

ISBN: 9783030738396

Standard No.: 10.1007/978-3-030-73839-6doiSubjects--Topical Terms:

532051
Logic, Symbolic and mathematical.

LC Class. No.: QA9 / .E33 2021

Dewey Class. No.: 511.3

Mathematical logic
LDR:03365nmm a2200361 a 4500 001 2240853
003 DE-He213
005 20210528023621.0
006 m d
007 cr nn 008maaau
008 211111s2021 sz s 0 eng d
020 $a 9783030738396 $q (electronic bk.)
020 $a 9783030738389 $q (paper)
024 7 $a 10.1007/978-3-030-73839-6 $2 doi
035 $a 978-3-030-73839-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA9 $b .E33 2021
072 7 $a PBC $2 bicssc
072 7 $a MAT018000 $2 bisacsh
072 7 $a PBC $2 thema
072 7 $a PBCD $2 thema
082 0 4 $a 511.3 $2 23
090 $a QA9 $b .E15 2021
100 1 $a Ebbinghaus, Heinz-Dieter. $3 1067192
245 1 0 $a Mathematical logic $h [electronic resource] / $c by Heinz-Dieter Ebbinghaus, Jorg Flum, Wolfgang Thomas.
250 $a Third edition.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a ix, 304 p. : $b ill., digital ; $c 24 cm.
490 1 $a Graduate texts in mathematics, $x 0072-5285 ; $v 291
505 0 $a A -- I Introduction -- II Syntax of First-Order Languages -- III Semantics of First-Order Languages -- IV A Sequent Calculus -- V The Completeness Theorem -- VI The Lowenheim-Skolem and the Compactness Theorem -- VII The Scope of First-Order Logic -- VIII Syntactic Interpretations and Normal Forms -- B -- IX Extensions of First-Order Logic -- X Computability and Its Limitations -- XI Free Models and Logic Programming -- XII An Algebraic Characterization of Elementary Equivalence -- XIII Lindstrom's Theorems -- References -- List of Symbols -- Subject Index.
520 $a This textbook introduces first-order logic and its role in the foundations of mathematics by examining fundamental questions. What is a mathematical proof? How can mathematical proofs be justified? Are there limitations to provability? To what extent can machines carry out mathematical proofs? In answering these questions, this textbook explores the capabilities and limitations of algorithms and proof methods in mathematics and computer science. The chapters are carefully organized, featuring complete proofs and numerous examples throughout. Beginning with motivating examples, the book goes on to present the syntax and semantics of first-order logic. After providing a sequent calculus for this logic, a Henkin-type proof of the completeness theorem is given. These introductory chapters prepare the reader for the advanced topics that follow, such as Godel's Incompleteness Theorems, Trakhtenbrot's undecidability theorem, Lindstrom's theorems on the maximality of first-order logic, and results linking logic with automata theory. This new edition features many modernizations, as well as two additional important results: The decidability of Presburger arithmetic, and the decidability of the weak monadic theory of the successor function. Mathematical Logic is ideal for students beginning their studies in logic and the foundations of mathematics. Although the primary audience for this textbook will be graduate students or advanced undergraduates in mathematics or computer science, in fact the book has few formal prerequisites. It demands of the reader only mathematical maturity and experience with basic abstract structures, such as those encountered in discrete mathematics or algebra.
650 0 $a Logic, Symbolic and mathematical. $3 532051
650 1 4 $a Mathematical Logic and Foundations. $3 892656
650 2 4 $a Mathematics of Computing. $3 891213
700 1 $a Flum, Jorg. $3 544196
700 1 $a Thomas, Wolfgang. $3 1070800
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Graduate texts in mathematics ; $v 291. $3 3496174
856 4 0 $u https://doi.org/10.1007/978-3-030-73839-6
950 $a Mathematics and Statistics (SpringerNature-11649)