Reverse Mathematics : : Proofs from the Inside Out / / John Stillwell.
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...
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Stillwell, John, author. aut http://id.loc.gov/vocabulary/relators/aut Reverse Mathematics : Proofs from the Inside Out / John Stillwell. Princeton, NJ : Princeton University Press, [2018] ©2018 1 online resource (200 p.) : 5 halftones. 30 line illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Frontmatter -- Contents -- Preface -- 1. Historical Introduction -- 2. Classical Arithmetization -- 3. Classical Analysis -- 4. Computability -- 5. Arithmetization of Computation -- 6. Arithmetical Comprehension -- 7. Recursive Comprehension -- 8. A Bigger Picture -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 27. Sep 2021) Reverse mathematics. MATHEMATICS / History & Philosophy. bisacsh Stillwell, John, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2018 9783110606591 print 9780691177175 https://doi.org/10.1515/9781400889037?locatt=mode:legacy https://www.degruyter.com/isbn/9781400889037 Cover https://www.degruyter.com/document/cover/isbn/9781400889037/original |
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English |
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Stillwell, John, Stillwell, John, |
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Stillwell, John, Stillwell, John, Reverse Mathematics : Proofs from the Inside Out / Frontmatter -- Contents -- Preface -- 1. Historical Introduction -- 2. Classical Arithmetization -- 3. Classical Analysis -- 4. Computability -- 5. Arithmetization of Computation -- 6. Arithmetical Comprehension -- 7. Recursive Comprehension -- 8. A Bigger Picture -- Bibliography -- Index |
author_facet |
Stillwell, John, Stillwell, John, Stillwell, John, Stillwell, John, |
author_variant |
j s js j s js |
author_role |
VerfasserIn VerfasserIn |
author2 |
Stillwell, John, Stillwell, John, |
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j s js j s js |
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MitwirkendeR MitwirkendeR |
author_sort |
Stillwell, John, |
title |
Reverse Mathematics : Proofs from the Inside Out / |
title_sub |
Proofs from the Inside Out / |
title_full |
Reverse Mathematics : Proofs from the Inside Out / John Stillwell. |
title_fullStr |
Reverse Mathematics : Proofs from the Inside Out / John Stillwell. |
title_full_unstemmed |
Reverse Mathematics : Proofs from the Inside Out / John Stillwell. |
title_auth |
Reverse Mathematics : Proofs from the Inside Out / |
title_alt |
Frontmatter -- Contents -- Preface -- 1. Historical Introduction -- 2. Classical Arithmetization -- 3. Classical Analysis -- 4. Computability -- 5. Arithmetization of Computation -- 6. Arithmetical Comprehension -- 7. Recursive Comprehension -- 8. A Bigger Picture -- Bibliography -- Index |
title_new |
Reverse Mathematics : |
title_sort |
reverse mathematics : proofs from the inside out / |
publisher |
Princeton University Press, |
publishDate |
2018 |
physical |
1 online resource (200 p.) : 5 halftones. 30 line illus. Issued also in print. |
contents |
Frontmatter -- Contents -- Preface -- 1. Historical Introduction -- 2. Classical Arithmetization -- 3. Classical Analysis -- 4. Computability -- 5. Arithmetization of Computation -- 6. Arithmetical Comprehension -- 7. Recursive Comprehension -- 8. A Bigger Picture -- Bibliography -- Index |
isbn |
9781400889037 9783110606591 9780691177175 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA9 |
callnumber-sort |
QA 19.25 S75 42020 |
url |
https://doi.org/10.1515/9781400889037?locatt=mode:legacy https://www.degruyter.com/isbn/9781400889037 https://www.degruyter.com/document/cover/isbn/9781400889037/original |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
511 - General principles of mathematics |
dewey-full |
511.3 |
dewey-sort |
3511.3 |
dewey-raw |
511.3 |
dewey-search |
511.3 |
doi_str_mv |
10.1515/9781400889037?locatt=mode:legacy |
oclc_num |
1012849815 |
work_keys_str_mv |
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Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2018 |
is_hierarchy_title |
Reverse Mathematics : Proofs from the Inside Out / |
container_title |
Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2018 |
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