國立高雄大學圖資館 |

Language: English

Back

Mathematical logicon numbers, sets, ...

Kossak, Roman.

Mathematical logicon numbers, sets, structures, and symmetry /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mathematical logicby Roman Kossak.
Reminder of title:	on numbers, sets, structures, and symmetry /
Author:	Kossak, Roman.
Published:	Cham :Springer International Publishing :2018.
Description:	xiii, 186 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Logic, Symbolic and mathematical.
Online resource:	https://doi.org/10.1007/978-3-319-97298-5
ISBN:	9783319972985$q(electronic bk.)

Mathematical logicon numbers, sets, structures, and symmetry /
Kossak, Roman.

Mathematical logicon numbers, sets, structures, and symmetry /[electronic resource] :by Roman Kossak. - Cham :Springer International Publishing :2018. - xiii, 186 p. :ill., digital ;24 cm. - Springer graduate texts in philosophy ;v.3. - Springer graduate texts in philosophy ;v.1..

Chapter1. Mathematical Logic -- Chapter2. Logical Seeing -- Chapter3. What is a Number? -- Chapter4. Number Structures -- Chapter5. Points, Lines -- Chapter6. Set Theory -- Chapter7. Relations -- Chapter8. Definable Elements and Constants -- Chapter9. Minimal and Order-Minimal Structures -- Chapter10. Geometry of Definable Sets -- Chapter11. Where Do Structures Come From? -- Chapter12. Elementary Extensions and Symmetries -- Chapter13. Tame vs. Wild -- Chapter14. First-order Properties -- Chapter15. Symmetries and Logical Visibility One More Time.

This book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Its first part, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. The exposition does not assume any prerequisites; it is rigorous, but as informal as possible. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. Although more advanced, this second part is accessible to the reader who is either already familiar with basic mathematical logic, or has carefully read the first part of the book. Classical developments in model theory, including the Compactness Theorem and its uses, are discussed. Other topics include tameness, minimality, and order minimality of structures. The book can be used as an introduction to model theory, but unlike standard texts, it does not require familiarity with abstract algebra. This book will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.

ISBN: 9783319972985$q(electronic bk.)

Standard No.: 10.1007/978-3-319-97298-5doiSubjects--Topical Terms:

180452
Logic, Symbolic and mathematical.

LC Class. No.: QA9 / .K67 2018

Dewey Class. No.: 511.3

Mathematical logicon numbers, sets, structures, and symmetry /
LDR:03150nmm a2200337 a 4500 001 544864
003 DE-He213
005 20190319143119.0
006 m d
007 cr nn 008maaau
008 190508s2018 gw s 0 eng d
020 $a 9783319972985$q(electronic bk.)
020 $a 9783319972978$q(paper)
024 7 $a 10.1007/978-3-319-97298-5 $2 doi
035 $a 978-3-319-97298-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA9 $b .K67 2018
072 7 $a PBB $2 bicssc
072 7 $a MAT015000 $2 bisacsh
072 7 $a PBB $2 thema
082 0 4 $a 511.3 $2 23
090 $a QA9 $b .K86 2018
100 1 $a Kossak, Roman. $3 787687
245 1 0 $a Mathematical logic $h [electronic resource] : $b on numbers, sets, structures, and symmetry / $c by Roman Kossak.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a xiii, 186 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer graduate texts in philosophy ; $v v.3
505 0 $a Chapter1. Mathematical Logic -- Chapter2. Logical Seeing -- Chapter3. What is a Number? -- Chapter4. Number Structures -- Chapter5. Points, Lines -- Chapter6. Set Theory -- Chapter7. Relations -- Chapter8. Definable Elements and Constants -- Chapter9. Minimal and Order-Minimal Structures -- Chapter10. Geometry of Definable Sets -- Chapter11. Where Do Structures Come From? -- Chapter12. Elementary Extensions and Symmetries -- Chapter13. Tame vs. Wild -- Chapter14. First-order Properties -- Chapter15. Symmetries and Logical Visibility One More Time.
520 $a This book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Its first part, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. The exposition does not assume any prerequisites; it is rigorous, but as informal as possible. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. Although more advanced, this second part is accessible to the reader who is either already familiar with basic mathematical logic, or has carefully read the first part of the book. Classical developments in model theory, including the Compactness Theorem and its uses, are discussed. Other topics include tameness, minimality, and order minimality of structures. The book can be used as an introduction to model theory, but unlike standard texts, it does not require familiarity with abstract algebra. This book will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.
650 0 $a Logic, Symbolic and mathematical. $3 180452
650 0 $a Mathematics $x Philosophy. $3 187658
650 1 4 $a Philosophy of Mathematics. $3 745264
650 2 4 $a Mathematical Logic and Foundations. $3 274479
650 2 4 $a Arithmetic and Logic Structures. $3 276274
650 2 4 $a Logic. $3 180785
650 2 4 $a Applications of Mathematics. $3 273744
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Springer graduate texts in philosophy ; $v v.1. $3 750582
856 4 0 $u https://doi.org/10.1007/978-3-319-97298-5
950 $a Religion and Philosophy (Springer-41175)