The logic of infinity:
Few mathematical results capture the imagination like Georg Cantor's groundbreaking work on infinity in the late nineteenth century. This opened the door to an intricate axiomatic theory of sets which was born in the decades that followed. Written for the motivated novice, this book provides an...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2014
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| Subjects: | |
| Online Access: | BSB01 FHN01 URL des Erstveröffentlichers |
| Summary: | Few mathematical results capture the imagination like Georg Cantor's groundbreaking work on infinity in the late nineteenth century. This opened the door to an intricate axiomatic theory of sets which was born in the decades that followed. Written for the motivated novice, this book provides an overview of key ideas in set theory, bridging the gap between technical accounts of mathematical foundations and popular accounts of logic. Readers will learn of the formal construction of the classical number systems, from the natural numbers to the real numbers and beyond, and see how set theory has evolved to analyse such deep questions as the status of the continuum hypothesis and the axiom of choice. Remarks and digressions introduce the reader to some of the philosophical aspects of the subject and to adjacent mathematical topics. The rich, annotated bibliography encourages the dedicated reader to delve into what is now a vast literature |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xxiv, 473 pages) |
| ISBN: | 9781107415614 |
| DOI: | 10.1017/CBO9781107415614 |
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| 505 | 8 | |a Introduction -- Logical foundations -- Avoiding Russell's paradox -- Further axioms -- Relations and order -- Ordinal numbers and the axiom of infinity -- Infinite arithmetic -- Cardinal numbers -- The axiom of choice and the continuum hypothesis -- Models -- From Gödel to Cohen. Peano arithmetic ; Zermelo-Fraenkel set theory ; Gödel's incompleteness theorems -- Bibliography -- Index | |
| 520 | |a Few mathematical results capture the imagination like Georg Cantor's groundbreaking work on infinity in the late nineteenth century. This opened the door to an intricate axiomatic theory of sets which was born in the decades that followed. Written for the motivated novice, this book provides an overview of key ideas in set theory, bridging the gap between technical accounts of mathematical foundations and popular accounts of logic. Readers will learn of the formal construction of the classical number systems, from the natural numbers to the real numbers and beyond, and see how set theory has evolved to analyse such deep questions as the status of the continuum hypothesis and the axiom of choice. Remarks and digressions introduce the reader to some of the philosophical aspects of the subject and to adjacent mathematical topics. The rich, annotated bibliography encourages the dedicated reader to delve into what is now a vast literature | ||
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| author_facet | Sheppard, Barnaby |
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| contents | Introduction -- Logical foundations -- Avoiding Russell's paradox -- Further axioms -- Relations and order -- Ordinal numbers and the axiom of infinity -- Infinite arithmetic -- Cardinal numbers -- The axiom of choice and the continuum hypothesis -- Models -- From Gödel to Cohen. Peano arithmetic ; Zermelo-Fraenkel set theory ; Gödel's incompleteness theorems -- Bibliography -- Index |
| ctrlnum | (ZDB-20-CBO)CR9781107415614 (OCoLC)900369685 (DE-599)BVBBV043943570 |
| 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 |
| doi_str_mv | 10.1017/CBO9781107415614 |
| format | Electronic eBook |
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| id | DE-604.BV043943570 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:19Z |
| institution | BVB |
| isbn | 9781107415614 |
| language | English |
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| physical | 1 online resource (xxiv, 473 pages) |
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| publishDate | 2014 |
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| publisher | Cambridge University Press |
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| spelling | Sheppard, Barnaby Verfasser aut The logic of infinity Barnaby Sheppard Cambridge Cambridge University Press 2014 1 online resource (xxiv, 473 pages) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) Introduction -- Logical foundations -- Avoiding Russell's paradox -- Further axioms -- Relations and order -- Ordinal numbers and the axiom of infinity -- Infinite arithmetic -- Cardinal numbers -- The axiom of choice and the continuum hypothesis -- Models -- From Gödel to Cohen. Peano arithmetic ; Zermelo-Fraenkel set theory ; Gödel's incompleteness theorems -- Bibliography -- Index Few mathematical results capture the imagination like Georg Cantor's groundbreaking work on infinity in the late nineteenth century. This opened the door to an intricate axiomatic theory of sets which was born in the decades that followed. Written for the motivated novice, this book provides an overview of key ideas in set theory, bridging the gap between technical accounts of mathematical foundations and popular accounts of logic. Readers will learn of the formal construction of the classical number systems, from the natural numbers to the real numbers and beyond, and see how set theory has evolved to analyse such deep questions as the status of the continuum hypothesis and the axiom of choice. Remarks and digressions introduce the reader to some of the philosophical aspects of the subject and to adjacent mathematical topics. The rich, annotated bibliography encourages the dedicated reader to delve into what is now a vast literature Set theory Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Axiomatische Mengenlehre (DE-588)4143743-3 gnd rswk-swf Axiomatische Mengenlehre (DE-588)4143743-3 s Mathematische Logik (DE-588)4037951-6 s DE-604 Erscheint auch als Druckausgabe 978-1-107-05831-6 Erscheint auch als Druckausgabe 978-1-107-67866-8 https://doi.org/10.1017/CBO9781107415614 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Sheppard, Barnaby The logic of infinity Introduction -- Logical foundations -- Avoiding Russell's paradox -- Further axioms -- Relations and order -- Ordinal numbers and the axiom of infinity -- Infinite arithmetic -- Cardinal numbers -- The axiom of choice and the continuum hypothesis -- Models -- From Gödel to Cohen. Peano arithmetic ; Zermelo-Fraenkel set theory ; Gödel's incompleteness theorems -- Bibliography -- Index Set theory Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd Axiomatische Mengenlehre (DE-588)4143743-3 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4143743-3 |
| title | The logic of infinity |
| title_auth | The logic of infinity |
| title_exact_search | The logic of infinity |
| title_full | The logic of infinity Barnaby Sheppard |
| title_fullStr | The logic of infinity Barnaby Sheppard |
| title_full_unstemmed | The logic of infinity Barnaby Sheppard |
| title_short | The logic of infinity |
| title_sort | the logic of infinity |
| topic | Set theory Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd Axiomatische Mengenlehre (DE-588)4143743-3 gnd |
| topic_facet | Set theory Logic, Symbolic and mathematical Mathematische Logik Axiomatische Mengenlehre |
| url | https://doi.org/10.1017/CBO9781107415614 |
| work_keys_str_mv | AT sheppardbarnaby thelogicofinfinity |