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| fixed length control field |
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| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
210128b xxu||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780691196411 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
511.3 |
| Item number |
STI |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Stillwell, John |
| 245 ## - TITLE STATEMENT |
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| Title |
Reverse mathematics : proofs from the inside out |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Name of publisher, distributor, etc |
Princeton University Press |
| Date of publication, distribution, etc |
2018 |
| Place of publication, distribution, etc |
Princeton |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xiii, 182 p. |
| Other physical details |
ill. |
| Dimensions |
24 cm |
| 365 ## - TRADE PRICE |
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| Price amount |
18.95 |
| Price type code |
USD |
| Unit of pricing |
76.50 |
| 490 ## - SERIES STATEMENT |
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| Series statement |
ProQuest Ebook Central |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 520 ## - SUMMARY, ETC. |
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| 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. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Reverse mathematics |
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| Topical term or geographic name as entry element |
Arithmetization of Computation |
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| Topical term or geographic name as entry element |
Computability |
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| Topical term or geographic name as entry element |
Hillbert's Axioms |
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| Topical term or geographic name as entry element |
Bolzano - Weierstrass theorem |
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| Topical term or geographic name as entry element |
Cantor set |
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| Topical term or geographic name as entry element |
Comprehension arithmetical |
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| Topical term or geographic name as entry element |
Extreme value theorem |
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| Topical term or geographic name as entry element |
Recursive comprehension |
|
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| Topical term or geographic name as entry element |
Set existence axiom |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
|
| Item type |
Books |