Reverse Mathematics: Proofs from the Inside Out
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...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[2018]
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| Schlagworte: | |
| Online-Zugang: | FAW01 FHA01 FKE01 FLA01 UPA01 FAB01 FCO01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed 29. Aug 2018) |
| Beschreibung: | 1 online resource 5 halftones. 30 line illus |
| ISBN: | 9781400889037 |
| DOI: | 10.1515/9781400889037 |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Stillwell, John |
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| dewey-full | 511.3 |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV045928908 |
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| indexdate | 2024-07-10T08:30:37Z |
| institution | BVB |
| isbn | 9781400889037 |
| language | English |
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| spelling | Stillwell, John Verfasser aut Reverse Mathematics Proofs from the Inside Out John Stillwell Princeton, NJ Princeton University Press [2018] © 2018 1 online resource 5 halftones. 30 line illus txt rdacontent c rdamedia cr rdacarrier Description based on online resource; title from PDF title page (publisher's Web site, viewed 29. Aug 2018) 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 In English Reverse mathematics Beweistheorie (DE-588)4145177-6 gnd rswk-swf Beweistheorie (DE-588)4145177-6 s 1\p DE-604 https://doi.org/10.1515/9781400889037 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Stillwell, John Reverse Mathematics Proofs from the Inside Out Reverse mathematics Beweistheorie (DE-588)4145177-6 gnd |
| subject_GND | (DE-588)4145177-6 |
| title | Reverse Mathematics Proofs from the Inside Out |
| title_auth | Reverse Mathematics Proofs from the Inside Out |
| title_exact_search | Reverse Mathematics 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_short | Reverse Mathematics |
| title_sort | reverse mathematics proofs from the inside out |
| title_sub | Proofs from the Inside Out |
| topic | Reverse mathematics Beweistheorie (DE-588)4145177-6 gnd |
| topic_facet | Reverse mathematics Beweistheorie |
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