Axiomatic Set Theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1973
|
| Schriftenreihe: | Graduate Texts in Mathematics
8 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This text deals with three basic techniques for constructing models of Zermelo-Fraenkel set theory: relative constructibility, Cohen's forcing, and Scott-Solovay's method of Boolean valued models. Our main concern will be the development of a unified theory that encompasses these techniques in one comprehensive framework. Consequently we will focus on certain fundamental and intrinsic relations between these methods of model construction. Extensive applications will not be treated here. This text is a continuation of our book, "Introduction to Axiomatic Set Theory," Springer-Verlag, 1971; indeed the two texts were originally planned as a single volume. The content of this volume is essentially that of a course taught by the first author at the University of Illinois in the spring of 1969. From the first author's lectures, a first draft was prepared by Klaus Gloede with the assistance of Donald Pelletier and the second author. This draft was then rcvised by the first author assisted by Hisao Tanaka. The introductory material was prepared by the second author who was also responsible for the general style of exposition throughout the text. We have included in the introductory material all the results from Boolean algebra and topology that we need. When notation from our first volume is introduced, it is accompanied with a deflnition, usually in a footnote. Consequently a reader who is familiar with elementary set theory will find this text quite self-contained |
| Beschreibung: | 1 Online-Ressource (238p) |
| ISBN: | 9781468487510 9780387900506 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4684-8751-0 |
Internformat
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| 500 | |a This text deals with three basic techniques for constructing models of Zermelo-Fraenkel set theory: relative constructibility, Cohen's forcing, and Scott-Solovay's method of Boolean valued models. Our main concern will be the development of a unified theory that encompasses these techniques in one comprehensive framework. Consequently we will focus on certain fundamental and intrinsic relations between these methods of model construction. Extensive applications will not be treated here. This text is a continuation of our book, "Introduction to Axiomatic Set Theory," Springer-Verlag, 1971; indeed the two texts were originally planned as a single volume. The content of this volume is essentially that of a course taught by the first author at the University of Illinois in the spring of 1969. From the first author's lectures, a first draft was prepared by Klaus Gloede with the assistance of Donald Pelletier and the second author. This draft was then rcvised by the first author assisted by Hisao Tanaka. The introductory material was prepared by the second author who was also responsible for the general style of exposition throughout the text. We have included in the introductory material all the results from Boolean algebra and topology that we need. When notation from our first volume is introduced, it is accompanied with a deflnition, usually in a footnote. Consequently a reader who is familiar with elementary set theory will find this text quite self-contained | ||
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Takeuti, Gaisi 1926-2017 |
| author_GND | (DE-588)107888580 (DE-588)172476011 |
| author_facet | Takeuti, Gaisi 1926-2017 |
| author_role | aut |
| author_sort | Takeuti, Gaisi 1926-2017 |
| author_variant | g t gt |
| building | Verbundindex |
| bvnumber | BV042421152 |
| classification_tum | MAT 000 |
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| ctrlnum | (OCoLC)1185220270 (DE-599)BVBBV042421152 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4684-8751-0 |
| format | Electronic eBook |
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| id | DE-604.BV042421152 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468487510 9780387900506 |
| issn | 0072-5285 |
| language | English |
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| publishDate | 1973 |
| publishDateSearch | 1973 |
| publishDateSort | 1973 |
| publisher | Springer New York |
| record_format | marc |
| series | Graduate Texts in Mathematics |
| series2 | Graduate Texts in Mathematics |
| spelling | Takeuti, Gaisi 1926-2017 Verfasser (DE-588)107888580 aut Axiomatic Set Theory by Gaisi Takeuti, Wilson M. Zaring New York, NY Springer New York 1973 1 Online-Ressource (238p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 8 0072-5285 This text deals with three basic techniques for constructing models of Zermelo-Fraenkel set theory: relative constructibility, Cohen's forcing, and Scott-Solovay's method of Boolean valued models. Our main concern will be the development of a unified theory that encompasses these techniques in one comprehensive framework. Consequently we will focus on certain fundamental and intrinsic relations between these methods of model construction. Extensive applications will not be treated here. This text is a continuation of our book, "Introduction to Axiomatic Set Theory," Springer-Verlag, 1971; indeed the two texts were originally planned as a single volume. The content of this volume is essentially that of a course taught by the first author at the University of Illinois in the spring of 1969. From the first author's lectures, a first draft was prepared by Klaus Gloede with the assistance of Donald Pelletier and the second author. This draft was then rcvised by the first author assisted by Hisao Tanaka. The introductory material was prepared by the second author who was also responsible for the general style of exposition throughout the text. We have included in the introductory material all the results from Boolean algebra and topology that we need. When notation from our first volume is introduced, it is accompanied with a deflnition, usually in a footnote. Consequently a reader who is familiar with elementary set theory will find this text quite self-contained Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Axiomatische Mengenlehre (DE-588)4143743-3 gnd rswk-swf Mengenlehre (DE-588)4074715-3 gnd rswk-swf Axiomatik (DE-588)4004038-0 gnd rswk-swf Mengenlehre (DE-588)4074715-3 s Axiomatik (DE-588)4004038-0 s 1\p DE-604 Axiomatische Mengenlehre (DE-588)4143743-3 s 2\p DE-604 Zaring, Wilson M. 1926- Sonstige (DE-588)172476011 oth Graduate Texts in Mathematics 8 (DE-604)BV000000067 8 https://doi.org/10.1007/978-1-4684-8751-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Takeuti, Gaisi 1926-2017 Axiomatic Set Theory Graduate Texts in Mathematics Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Axiomatische Mengenlehre (DE-588)4143743-3 gnd Mengenlehre (DE-588)4074715-3 gnd Axiomatik (DE-588)4004038-0 gnd |
| subject_GND | (DE-588)4143743-3 (DE-588)4074715-3 (DE-588)4004038-0 |
| title | Axiomatic Set Theory |
| title_auth | Axiomatic Set Theory |
| title_exact_search | Axiomatic Set Theory |
| title_full | Axiomatic Set Theory by Gaisi Takeuti, Wilson M. Zaring |
| title_fullStr | Axiomatic Set Theory by Gaisi Takeuti, Wilson M. Zaring |
| title_full_unstemmed | Axiomatic Set Theory by Gaisi Takeuti, Wilson M. Zaring |
| title_short | Axiomatic Set Theory |
| title_sort | axiomatic set theory |
| topic | Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Axiomatische Mengenlehre (DE-588)4143743-3 gnd Mengenlehre (DE-588)4074715-3 gnd Axiomatik (DE-588)4004038-0 gnd |
| topic_facet | Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Axiomatische Mengenlehre Mengenlehre Axiomatik |
| url | https://doi.org/10.1007/978-1-4684-8751-0 |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT takeutigaisi axiomaticsettheory AT zaringwilsonm axiomaticsettheory |