Introduction to Incompleteness (Record no. 62917)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03915nam a22005175i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-031-64217-3 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20251030112923.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240831s2024 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783031642173 |
| -- | 978-3-031-64217-3 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-031-64217-3 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA8.9-10.3 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBCD |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBC |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT018000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBCD |
| Source | thema |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBC |
| Source | thema |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Batzoglou, Serafim. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 83313 |
| 245 10 - TITLE STATEMENT | |
| Title | Introduction to Incompleteness |
| Medium | [electronic resource] : |
| Remainder of title | From Gödel's Theorems to Forcing and the Continuum Hypothesis / |
| Statement of responsibility, etc. | by Serafim Batzoglou. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. 2024. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Cham : |
| Name of producer, publisher, distributor, manufacturer | Springer Nature Switzerland : |
| -- | Imprint: Birkhäuser, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2024. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XI, 302 p. 13 illus. |
| Other physical details | online resource. |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS | |
| File type | text file |
| Encoding format | |
| Source | rda |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Part 1: Godel's Theorems -- Formal Axiomatic Systems -- Peano Arithmetic and Recursive Functions -- Godel's Incompleteness Theorems -- Structures, Models, and Satisfaction -- Completeness and Compactness Theorems -- Completeness and Peano Arithmetic -- The Lucas-Penrose Arguments -- Part II: Incompleteness in arithmetic and set theory -- Incompleteness in Finite Combinatorics -- Consistency of PA and E0 Induction -- Set Theory -- Independence of CH--forcing -- Independence of CH--forcing CH and -CH. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | Incompleteness is a fascinating phenomenon at the intersection of mathematical foundations, computer science, and epistemology that places a limit on what is provable. However, despite its importance, it is often overlooked in the mathematics curricula because it is difficult to teach. This book aims to help bridge this pedagogical gap by providing a complete and accessible technical exposition of incompleteness for a wide audience. The author accomplishes this by making conceptually difficult proofs more approachable by providing intuitive explanations of the main ideas. Care is taken to emphasize the different layers of the mathematical argument – the layer within and the metalayer about an axiomatic system. Structurally, the book efficiently examines key results and arrives at some of the most interesting concepts as quickly as possible. It begins with Gödel's incompleteness theorems before continuing on to challenging concepts in the arithmetized completeness theorem, the Paris-Harrington theorem, and the independence of the continuum hypothesis. Other topics covered include the Lucas-Penrose arguments, ordinals and cardinals, and axiomatic set theory. Additionally, the author’s coverage of forcing is a notable addition to the existing literature. Introduction to Incompleteness will be of interest to researchers, students, and instructors looking for a resource to teach this topic. It may also be suitable for self-study. Knowledge of undergraduate-level theoretical mathematics or computer science is required, as well as a familiarity with abstract proofs. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 66195 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 66198 |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer Nature eBook |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031642166 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031642180 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031642197 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1007/978-3-031-64217-3">https://doi.org/10.1007/978-3-031-64217-3</a> |
| 912 ## - | |
| -- | ZDB-2-SMA |
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| -- | ZDB-2-SXMS |
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