東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

FindBook

Google Book

Amazon

博客來

An invitation to mathematical logic

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	An invitation to mathematical logic/ by David Marker.
作者:	Marker, David.
出版者:	Cham :Springer Nature Switzerland : : 2024.,
面頁冊數:	xviii, 357 p. :ill., digital ;24 cm.
內容註:	Introduction -- I. Truth and Proof -- 1 Languages, Structures and Theories -- 2 Embeddings and Substructures -- 3 Formal Proofs -- 4 Gödel's Completeness Theorem -- II. Elements of Model Theory -- 5 Compactness and Complete Theories -- 6 Ultraproducts -- 7 Quantifier Elimination -- 8 Model Theory of the Real Field -- III. Computability -- 9 Models of Computation -- 10 Universal Machines and Undecidability -- 11 Computably Enumerable and Arithmetic Sets -- 12 Turing Reducibility -- IV. Arithmetic and Incompleteness -- 13 Gödel's Incompleteness Theorems -- 14 Hilbert's 10th Problem -- 15 Peano Arithmetic and ϵ0 -- 16 Models of Arithmetic and Independence Results. - Appendices -- A Set Theory. - B Unique Readability. - C Real Algebra. -Bibliography. - Index.
Contained By:	Springer Nature eBook
標題:	Logic, Symbolic and mathematical. -
電子資源:	https://doi.org/10.1007/978-3-031-55368-4
ISBN:	9783031553684

An invitation to mathematical logic
Marker, David.

An invitation to mathematical logic[electronic resource] /by David Marker. - Cham :Springer Nature Switzerland :2024. - xviii, 357 p. :ill., digital ;24 cm. - Graduate texts in mathematics,3012197-5612 ;. - Graduate texts in mathematics ;301..

Introduction -- I. Truth and Proof -- 1 Languages, Structures and Theories -- 2 Embeddings and Substructures -- 3 Formal Proofs -- 4 Gödel's Completeness Theorem -- II. Elements of Model Theory -- 5 Compactness and Complete Theories -- 6 Ultraproducts -- 7 Quantifier Elimination -- 8 Model Theory of the Real Field -- III. Computability -- 9 Models of Computation -- 10 Universal Machines and Undecidability -- 11 Computably Enumerable and Arithmetic Sets -- 12 Turing Reducibility -- IV. Arithmetic and Incompleteness -- 13 Gödel's Incompleteness Theorems -- 14 Hilbert's 10th Problem -- 15 Peano Arithmetic and ϵ0 -- 16 Models of Arithmetic and Independence Results. - Appendices -- A Set Theory. - B Unique Readability. - C Real Algebra. -Bibliography. - Index.

In addition to covering the essentials, the author's intention in writing this text is to entice the reader to further study mathematical logic. There is no current "standard text" for a first graduate course in mathematical logic and this book will fill that gap. While there is more material than could be covered in a traditional one semester course, an instructor can cover the basics and still have the flexibility to choose several weeks' worth of interesting advanced topics that have been introduced. The text can and will be used by people in various courses with different sorts of perspectives. This versatility is one of the many appealing aspects of this book. A list of suggested portions to be covered in a single course is provided as well as a useful chart which maps chapter dependencies. Additionally, a motivated student will have ample material for further reading. New definitions, formalism, and syntax have been streamlined to engage the reader quickly into the heart of logic and to more sophisticated topics. Part I and Part IV center on foundational questions, while Part III establishes the fundamentals of computability. Part II develops model theory, highlighting the model theory of the fields of real and complex numbers. The interplay between logic and other areas of mathematics, notably algebra, number theory, and combinatorics, are illustrated in Chapters 5, 6, 8, 14, and 16. For most of the text, the only prerequisite is mathematical maturity. The material should be accessible to first year graduate students or advanced undergraduates in mathematics, graduate students in philosophy with a solid math background, or students in computer science who want a mathematical introduction to logic. Prior exposure to logic is helpful but not assumed.

ISBN: 9783031553684

Standard No.: 10.1007/978-3-031-55368-4doiSubjects--Topical Terms:

532051
Logic, Symbolic and mathematical.

LC Class. No.: QA9

Dewey Class. No.: 511.3

An invitation to mathematical logic
LDR:03621nmm a2200361 a 4500 001 2371690
003 DE-He213
005 20240507103542.0
006 m d
007 cr nn 008maaau
008 241127s2024 sz s 0 eng d
020 $a 9783031553684 $q (electronic bk.)
020 $a 9783031553677 $q (paper)
024 7 $a 10.1007/978-3-031-55368-4 $2 doi
035 $a 978-3-031-55368-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA9
072 7 $a PBCD $2 bicssc
072 7 $a PBC $2 bicssc
072 7 $a MAT018000 $2 bisacsh
072 7 $a PBCD $2 thema
072 7 $a PBC $2 thema
082 0 4 $a 511.3 $2 23
090 $a QA9 $b .M345 2024
100 1 $a Marker, David. $3 1073244
245 1 3 $a An invitation to mathematical logic $h [electronic resource] / $c by David Marker.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2024.
300 $a xviii, 357 p. : $b ill., digital ; $c 24 cm.
490 1 $a Graduate texts in mathematics, $x 2197-5612 ; $v 301
505 0 $a Introduction -- I. Truth and Proof -- 1 Languages, Structures and Theories -- 2 Embeddings and Substructures -- 3 Formal Proofs -- 4 Gödel's Completeness Theorem -- II. Elements of Model Theory -- 5 Compactness and Complete Theories -- 6 Ultraproducts -- 7 Quantifier Elimination -- 8 Model Theory of the Real Field -- III. Computability -- 9 Models of Computation -- 10 Universal Machines and Undecidability -- 11 Computably Enumerable and Arithmetic Sets -- 12 Turing Reducibility -- IV. Arithmetic and Incompleteness -- 13 Gödel's Incompleteness Theorems -- 14 Hilbert's 10th Problem -- 15 Peano Arithmetic and ϵ0 -- 16 Models of Arithmetic and Independence Results. - Appendices -- A Set Theory. - B Unique Readability. - C Real Algebra. -Bibliography. - Index.
520 $a In addition to covering the essentials, the author's intention in writing this text is to entice the reader to further study mathematical logic. There is no current "standard text" for a first graduate course in mathematical logic and this book will fill that gap. While there is more material than could be covered in a traditional one semester course, an instructor can cover the basics and still have the flexibility to choose several weeks' worth of interesting advanced topics that have been introduced. The text can and will be used by people in various courses with different sorts of perspectives. This versatility is one of the many appealing aspects of this book. A list of suggested portions to be covered in a single course is provided as well as a useful chart which maps chapter dependencies. Additionally, a motivated student will have ample material for further reading. New definitions, formalism, and syntax have been streamlined to engage the reader quickly into the heart of logic and to more sophisticated topics. Part I and Part IV center on foundational questions, while Part III establishes the fundamentals of computability. Part II develops model theory, highlighting the model theory of the fields of real and complex numbers. The interplay between logic and other areas of mathematics, notably algebra, number theory, and combinatorics, are illustrated in Chapters 5, 6, 8, 14, and 16. For most of the text, the only prerequisite is mathematical maturity. The material should be accessible to first year graduate students or advanced undergraduates in mathematics, graduate students in philosophy with a solid math background, or students in computer science who want a mathematical introduction to logic. Prior exposure to logic is helpful but not assumed.
650 0 $a Logic, Symbolic and mathematical. $3 532051
650 1 4 $a Mathematical Logic and Foundations. $3 892656
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Graduate texts in mathematics ; $v 301. $3 3717914
856 4 0 $u https://doi.org/10.1007/978-3-031-55368-4
950 $a Mathematics and Statistics (SpringerNature-11649)