語系:
繁體中文
English
說明(常見問題)
登入
回首頁
切換:
標籤
|
MARC模式
|
ISBD
Mathematical Logic
~
Ebbinghaus, Heinz-Dieter.
Mathematical Logic
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Mathematical Logic/ by Heinz-Dieter Ebbinghaus, Jörg Flum, Wolfgang Thomas.
作者:
Ebbinghaus, Heinz-Dieter.
其他作者:
Thomas, Wolfgang.
面頁冊數:
IX, 304 p. 17 illus.online resource. :
Contained By:
Springer Nature eBook
標題:
Mathematics of Computing. -
電子資源:
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, Jörg Flum, Wolfgang Thomas. - 3rd ed. 2021. - IX, 304 p. 17 illus.online resource. - Graduate Texts in Mathematics,2912197-5612 ;. - Graduate Texts in Mathematics,222.
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 Löwenheim–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 Lindström’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 Gödel's Incompleteness Theorems, Trakhtenbrot's undecidability theorem, Lindström'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:
669457
Mathematics of Computing.
LC Class. No.: QA8.9-10.3
Dewey Class. No.: 511.3
Mathematical Logic
LDR
:03712nam a22004215i 4500
001
1054907
003
DE-He213
005
20210908011746.0
007
cr nn 008mamaa
008
220103s2021 sz | s |||| 0|eng d
020
$a
9783030738396
$9
978-3-030-73839-6
024
7
$a
10.1007/978-3-030-73839-6
$2
doi
035
$a
978-3-030-73839-6
050
4
$a
QA8.9-10.3
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
100
1
$a
Ebbinghaus, Heinz-Dieter.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
1068007
245
1 0
$a
Mathematical Logic
$h
[electronic resource] /
$c
by Heinz-Dieter Ebbinghaus, Jörg Flum, Wolfgang Thomas.
250
$a
3rd ed. 2021.
264
1
$a
Cham :
$b
Springer International Publishing :
$b
Imprint: Springer,
$c
2021.
300
$a
IX, 304 p. 17 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
Graduate Texts in Mathematics,
$x
2197-5612 ;
$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 Löwenheim–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 Lindström’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 Gödel's Incompleteness Theorems, Trakhtenbrot's undecidability theorem, Lindström'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
2 4
$a
Mathematics of Computing.
$3
669457
650
1 4
$a
Mathematical Logic and Foundations.
$3
669393
650
0
$a
Computer science—Mathematics.
$3
1253519
650
0
$a
Mathematical logic.
$2
bicssc
$3
810627
700
1
$a
Thomas, Wolfgang.
$e
author.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
1279145
700
1
$a
Flum, Jörg.
$e
author.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
1279144
710
2
$a
SpringerLink (Online service)
$3
593884
773
0
$t
Springer Nature eBook
776
0 8
$i
Printed edition:
$z
9783030738389
776
0 8
$i
Printed edition:
$z
9783030738402
776
0 8
$i
Printed edition:
$z
9783030738419
830
0
$a
Graduate Texts in Mathematics,
$x
0072-5285 ;
$v
222
$3
1254915
856
4 0
$u
https://doi.org/10.1007/978-3-030-73839-6
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)
筆 0 讀者評論
多媒體
評論
新增評論
分享你的心得
Export
取書館別
處理中
...
變更密碼[密碼必須為2種組合(英文和數字)及長度為10碼以上]
登入