The foundations of mathematics in the theory of sets:
This 2001 book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of 'natural number�...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2000
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 82 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | This 2001 book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of 'natural number' and 'set'. This leads to an investigation of the logic of quantification over the universe of sets and a discussion of its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. The subject matter of the book falls on the borderline between philosophy and mathematics, and should appeal to both philosophers and mathematicians with an interest in the foundations of mathematics |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xx, 424 pages) |
| ISBN: | 9781139087124 |
| DOI: | 10.1017/CBO9781139087124 |
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| 505 | 8 | 0 | |t Preliminaries |t Idea of foundations for mathematics |t Simple arithmetic |t Basic set theory |t Semantics, ontology, and logic |t Principal axioms and definitions of set theory |t Cantorian set theory |t Cantorian finitism |t Axiomatic method |t Axiomatic set theory |t Euclidean set theory |t Euclidean finitism |t Euclidean theory of cardinality |t Euclidean theory of simply infinite systems |t Euclidean set theory from the cantorian standpoint |t Envoi |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Mayberry, John P. |
| author_facet | Mayberry, John P. |
| author_role | aut |
| author_sort | Mayberry, John P. |
| author_variant | j p m jp jpm |
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| bvnumber | BV043942095 |
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| contents | Preliminaries Idea of foundations for mathematics Simple arithmetic Basic set theory Semantics, ontology, and logic Principal axioms and definitions of set theory Cantorian set theory Cantorian finitism Axiomatic method Axiomatic set theory Euclidean set theory Euclidean finitism Euclidean theory of cardinality Euclidean theory of simply infinite systems Euclidean set theory from the cantorian standpoint Envoi |
| ctrlnum | (ZDB-20-CBO)CR9781139087124 (OCoLC)855562759 (DE-599)BVBBV043942095 |
| dewey-full | 511.3/22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/22 |
| dewey-search | 511.3/22 |
| dewey-sort | 3511.3 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| doi_str_mv | 10.1017/CBO9781139087124 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
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| isbn | 9781139087124 |
| language | English |
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| series2 | Encyclopedia of mathematics and its applications |
| spelling | Mayberry, John P. Verfasser aut The foundations of mathematics in the theory of sets J.P. Mayberry Cambridge Cambridge University Press 2000 1 online resource (xx, 424 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 82 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Preliminaries Idea of foundations for mathematics Simple arithmetic Basic set theory Semantics, ontology, and logic Principal axioms and definitions of set theory Cantorian set theory Cantorian finitism Axiomatic method Axiomatic set theory Euclidean set theory Euclidean finitism Euclidean theory of cardinality Euclidean theory of simply infinite systems Euclidean set theory from the cantorian standpoint Envoi This 2001 book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of 'natural number' and 'set'. This leads to an investigation of the logic of quantification over the universe of sets and a discussion of its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. The subject matter of the book falls on the borderline between philosophy and mathematics, and should appeal to both philosophers and mathematicians with an interest in the foundations of mathematics Set theory Mengenlehre (DE-588)4074715-3 gnd rswk-swf Mengenlehre (DE-588)4074715-3 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-17271-4 Erscheint auch als Druckausgabe 978-0-521-77034-7 https://doi.org/10.1017/CBO9781139087124 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mayberry, John P. The foundations of mathematics in the theory of sets Preliminaries Idea of foundations for mathematics Simple arithmetic Basic set theory Semantics, ontology, and logic Principal axioms and definitions of set theory Cantorian set theory Cantorian finitism Axiomatic method Axiomatic set theory Euclidean set theory Euclidean finitism Euclidean theory of cardinality Euclidean theory of simply infinite systems Euclidean set theory from the cantorian standpoint Envoi Set theory Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4074715-3 |
| title | The foundations of mathematics in the theory of sets |
| title_alt | Preliminaries Idea of foundations for mathematics Simple arithmetic Basic set theory Semantics, ontology, and logic Principal axioms and definitions of set theory Cantorian set theory Cantorian finitism Axiomatic method Axiomatic set theory Euclidean set theory Euclidean finitism Euclidean theory of cardinality Euclidean theory of simply infinite systems Euclidean set theory from the cantorian standpoint Envoi |
| title_auth | The foundations of mathematics in the theory of sets |
| title_exact_search | The foundations of mathematics in the theory of sets |
| title_full | The foundations of mathematics in the theory of sets J.P. Mayberry |
| title_fullStr | The foundations of mathematics in the theory of sets J.P. Mayberry |
| title_full_unstemmed | The foundations of mathematics in the theory of sets J.P. Mayberry |
| title_short | The foundations of mathematics in the theory of sets |
| title_sort | the foundations of mathematics in the theory of sets |
| topic | Set theory Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Set theory Mengenlehre |
| url | https://doi.org/10.1017/CBO9781139087124 |
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