Reverse mathematics : (Record no. 81391)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 07406cam a2200757 i 4500 |
| 001 - CONTROL NUMBER | |
| control field | on1012849815 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | OCoLC |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20220908100133.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr ||||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 171124s2018 njua ob 001 0 eng d |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | IDEBK |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | IDEBK |
| Modifying agency | N$T |
| -- | EBLCP |
| -- | YDX |
| -- | CNCGM |
| -- | MNW |
| -- | MUU |
| -- | IDB |
| -- | NRC |
| -- | INT |
| -- | DEGRU |
| -- | AU@ |
| -- | TSC |
| -- | OCLCQ |
| -- | WYU |
| -- | OCLCQ |
| -- | JSTOR |
| -- | OCLCQ |
| -- | MM9 |
| -- | UX1 |
| -- | OCLCQ |
| -- | IEEEE |
| -- | OCLCQ |
| -- | OCLCO |
| 066 ## - CHARACTER SETS PRESENT | |
| Alternate G0 or G1 character set | (S |
| 019 ## - | |
| -- | 1162046061 |
| -- | 1175629450 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 1400889030 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781400889037 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780691177175 |
| Qualifying information | (hardcover |
| -- | alk. paper) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 0691177171 |
| Qualifying information | (hardcover |
| -- | alk. paper) |
| 029 1# - OTHER SYSTEM CONTROL NUMBER (OCLC) | |
| OCLC library identifier | AU@ |
| System control number | 000061388128 |
| 029 1# - OTHER SYSTEM CONTROL NUMBER (OCLC) | |
| OCLC library identifier | GBVCP |
| System control number | 1011003759 |
| 029 1# - OTHER SYSTEM CONTROL NUMBER (OCLC) | |
| OCLC library identifier | AU@ |
| System control number | 000062004912 |
| 029 1# - OTHER SYSTEM CONTROL NUMBER (OCLC) | |
| OCLC library identifier | AU@ |
| System control number | 000062577688 |
| 029 1# - OTHER SYSTEM CONTROL NUMBER (OCLC) | |
| OCLC library identifier | AU@ |
| System control number | 000065054106 |
| 029 1# - OTHER SYSTEM CONTROL NUMBER (OCLC) | |
| OCLC library identifier | AU@ |
| System control number | 000067043333 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1012849815 |
| Canceled/invalid control number | (OCoLC)1162046061 |
| -- | (OCoLC)1175629450 |
| 037 ## - SOURCE OF ACQUISITION | |
| Stock number | 1050470 |
| Source of stock number/acquisition | MIL |
| 037 ## - SOURCE OF ACQUISITION | |
| Stock number | 22573/ctvc66xk3 |
| Source of stock number/acquisition | JSTOR |
| 037 ## - SOURCE OF ACQUISITION | |
| Stock number | 9452339 |
| Source of stock number/acquisition | IEEE |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA9.25 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 000000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 015000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 018000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 034000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | SCI |
| Subject category code subdivision | 034000 |
| Source | bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 511.3 |
| Edition number | 23 |
| 084 ## - OTHER CLASSIFICATION NUMBER | |
| Classification number | MAT015000 |
| -- | MAT000000 |
| -- | MAT018000 |
| -- | SCI034000 |
| Number source | bisacsh |
| 049 ## - LOCAL HOLDINGS (OCLC) | |
| Holding library | MAIN |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Stillwell, John, |
| Relator term | author. |
| 9 (RLIN) | 65032 |
| 245 10 - TITLE STATEMENT | |
| Title | Reverse mathematics : |
| Remainder of title | proofs from the inside out / |
| Statement of responsibility, etc. | John Stillwell. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Princeton : |
| Name of producer, publisher, distributor, manufacturer | Princeton University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | [2018] |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | �2018 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (xiii, 182 pages) |
| 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 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc. note | Includes bibliographical references and index. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Linkage | 880-01 |
| Formatted contents note | Historical introduction -- Classical arithmetization -- Classical analysis -- Computability -- Arithmetization of computation -- Arithmetical comprehension -- Recursive comprehension -- A bigger picture. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | "This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In Reverse Mathematics, John Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. Stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentieth-century arithmetization of logic and computation. Thus arithmetic in some sense underlies analysis, logic, and computation. Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the "right axiom" to prove it. By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics."-- |
| Assigning source | Provided by publisher |
| 588 0# - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Online resource; title from electronic title page (EBSCOHost, viewed March 14, 2018). |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | IEEE |
| Provenance (VM) [OBSOLETE] | IEEE Xplore Princeton University Press eBooks Library |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Reverse mathematics. |
| 9 (RLIN) | 65033 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Math�ematiques �a rebours. |
| 9 (RLIN) | 65034 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | MATHEMATICS |
| General subdivision | General. |
| Source of heading or term | bisacsh |
| 9 (RLIN) | 4635 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Reverse mathematics. |
| Source of heading or term | fast |
| Authority record control number or standard number | (OCoLC)fst01737141 |
| 9 (RLIN) | 65033 |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 9 (RLIN) | 3294 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Stillwell, John. |
| Title | Reverse mathematics. |
| Place, publisher, and date of publication | Princeton, New Jersey : Princeton University Press, [2018] |
| International Standard Book Number | 9780691177175 |
| Record control number | (DLC) 2017025264 |
| -- | (OCoLC)983825003 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ieeexplore.ieee.org/servlet/opac?bknumber=9452339">https://ieeexplore.ieee.org/servlet/opac?bknumber=9452339</a> |
| 880 00 - ALTERNATE GRAPHIC REPRESENTATION | |
| Linkage | 505-01/(S |
| g | Machine generated contents note: |
| -- | 1. |
| t | Historical Introduction -- |
| g | 1.1. |
| t | Euclid and the Parallel Axiom -- |
| g | 1.2. |
| t | Spherical and Non-Euclidean Geometry -- |
| g | 1.3. |
| t | Vector Geometry -- |
| g | 1.4. |
| t | Hilbert's Axioms -- |
| g | 1.5. |
| t | Well-ordering and the Axiom of Choice -- |
| g | 1.6. |
| t | Logic and Computability -- |
| g | 2. |
| t | Classical Arithmetization -- |
| g | 2.1. |
| t | From Natural to Rational Numbers -- |
| g | 2.2. |
| t | From Rationals to Reals -- |
| g | 2.3. |
| t | Completeness Properties of R -- |
| g | 2.4. |
| t | Functions and Sets -- |
| g | 2.5. |
| t | Continuous Functions -- |
| g | 2.6. |
| t | Peano Axioms -- |
| g | 2.7. |
| t | Language of PA -- |
| g | 2.8. |
| t | Arithmetically Definable Sets -- |
| g | 2.9. |
| t | Limits of Arithmetization -- |
| g | 3. |
| t | Classical Analysis -- |
| g | 3.1. |
| t | Limits -- |
| g | 3.2. |
| t | Algebraic Properties of Limits -- |
| g | 3.3. |
| t | Continuity and Intermediate Values -- |
| g | 3.4. |
| t | Bolzano-Weierstrass Theorem -- |
| g | 3.5. |
| t | Heine-Borel Theorem -- |
| g | 3.6. |
| t | Extreme Value Theorem -- |
| g | 3.7. |
| t | Uniform Continuity -- |
| g | 3.8. |
| t | Cantor Set -- |
| g | 3.9. |
| t | Trees in Analysis -- |
| g | 4. |
| t | Computability -- |
| g | 4.1. |
| t | Computability and Church's Thesis -- |
| g | 4.2. |
| t | Halting Problem -- |
| g | 4.3. |
| t | Computably Enumerable Sets -- |
| g | 4.4. |
| t | Computable Sequences in Analysis -- |
| g | 4.5. |
| t | Computable Tree with No Computable Path -- |
| g | 4.6. |
| t | Computability and Incompleteness -- |
| g | 4.7. |
| t | Computability and Analysis -- |
| g | 5. |
| t | Arithmetization of Computation -- |
| g | 5.1. |
| t | Formal Systems -- |
| g | 5.2. |
| t | Smullyan's Elementary Formal Systems -- |
| g | 5.3. |
| t | Notations for Positive Integers -- |
| g | 5.4. |
| t | Turing's Analysis of Computation -- |
| g | 5.5. |
| t | Operations on EFS-Generated Sets -- |
| g | 5.6. |
| t | Generating (SV(B01 Sets -- |
| g | 5.7. |
| t | EFS for (SV(B01 Relations -- |
| g | 5.8. |
| t | Arithmetizing Elementary Formal Systems -- |
| g | 5.9. |
| t | Arithmetizing Computable Enumeration -- |
| g | 5.10. |
| t | Arithmetizing Computable Analysis -- |
| g | 6. |
| t | Arithmetical Comprehension -- |
| g | 6.1. |
| t | Axiom System ACA0 -- |
| g | 6.2. |
| t | (SV(B01 and Arithmetical Comprehension -- |
| g | 6.3. |
| t | Completeness Properties in ACA0 -- |
| g | 6.4. |
| t | Arithmetization of Trees -- |
| g | 6.5. |
| t | Konig Infinity Lemma -- |
| g | 6.6. |
| t | Ramsey Theory -- |
| g | 6.7. |
| t | Some Results from Logic -- |
| g | 6.8. |
| t | Peano Arithmetic in ACA0 -- |
| g | 7. |
| t | Recursive Comprehension -- |
| g | 7.1. |
| t | Axiom System RCA0 -- |
| g | 7.2. |
| t | Real Numbers and Continuous Functions -- |
| g | 7.3. |
| t | Intermediate Value Theorem -- |
| g | 7.4. |
| t | Cantor Set Revisited -- |
| g | 7.5. |
| t | From Heine-Borel to Weak Konig Lemma -- |
| g | 7.6. |
| t | From Weak Konig Lemma to Heine-Borel -- |
| g | 7.7. |
| t | Uniform Continuity -- |
| g | 7.8. |
| t | From Weak Konig to Extreme Value -- |
| g | 7.9. |
| t | Theorems of WKL0 -- |
| g | 7.10. |
| t | WKL0, ACA0, and Beyond -- |
| g | 8. |
| t | Bigger Picture -- |
| g | 8.1. |
| t | Constructive Mathematics -- |
| g | 8.2. |
| t | Predicate Logic -- |
| g | 8.3. |
| t | Varieties of Incompleteness -- |
| g | 8.4. |
| t | Computability -- |
| g | 8.5. |
| t | Set Theory -- |
| g | 8.6. |
| t | Concepts of "Depth." |
| 938 ## - | |
| -- | De Gruyter |
| -- | DEGR |
| -- | 9781400889037 |
| 938 ## - | |
| -- | YBP Library Services |
| -- | YANK |
| -- | 14643228 |
| 938 ## - | |
| -- | EBL - Ebook Library |
| -- | EBLB |
| -- | EBL5199840 |
| 938 ## - | |
| -- | ProQuest MyiLibrary Digital eBook Collection |
| -- | IDEB |
| -- | cis39138779 |
| 938 ## - | |
| -- | EBSCOhost |
| -- | EBSC |
| -- | 1550094 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | eBooks |
| 994 ## - | |
| -- | 92 |
| -- | INTKS |
No items available.