Nonstandard Analysis, Axiomatically:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2004
|
| Schriftenreihe: | Springer Monographs in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In the aftermath of the discoveries in foundations of mathematiC's there was surprisingly little effect on mathematics as a whole. If one looks at stan dard textbooks in different mathematical disciplines, especially those closer to what is referred to as applied mathematics, there is little trace of those developments outside of mathematical logic and model theory. But it seems fair to say that there is a widespread conviction that the principles embodied in the Zermelo - Fraenkel theory with Choice (ZFC) are a correct description of the set theoretic underpinnings of mathematics. In most textbooks of the kind referred to above, there is, of course, no discussion of these matters, and set theory is assumed informally, although more advanced principles like Choice or sometimes Replacement are often mentioned explicitly. This implicitly fixes a point of view of the mathemat ical universe which is at odds with the results in foundations. For example most mathematicians still take it for granted that the real number system is uniquely determined up to isomorphism, which is a correct point of view as long as one does not accept to look at "unnatural" interpretations of the membership relation |
| Beschreibung: | 1 Online-Ressource (XVI, 410 p) |
| ISBN: | 9783662089989 9783642060779 |
| ISSN: | 1439-7382 |
| DOI: | 10.1007/978-3-662-08998-9 |
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Datensatz im Suchindex
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-08998-9 |
| format | Electronic eBook |
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| id | DE-604.BV042423414 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662089989 9783642060779 |
| issn | 1439-7382 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858831 |
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| physical | 1 Online-Ressource (XVI, 410 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2004 |
| publishDateSearch | 2004 |
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| publisher | Springer Berlin Heidelberg |
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| series2 | Springer Monographs in Mathematics |
| spelling | Kanovei, Vladimir Verfasser aut Nonstandard Analysis, Axiomatically by Vladimir Kanovei, Michael Reeken Berlin, Heidelberg Springer Berlin Heidelberg 2004 1 Online-Ressource (XVI, 410 p) txt rdacontent c rdamedia cr rdacarrier Springer Monographs in Mathematics 1439-7382 In the aftermath of the discoveries in foundations of mathematiC's there was surprisingly little effect on mathematics as a whole. If one looks at stan dard textbooks in different mathematical disciplines, especially those closer to what is referred to as applied mathematics, there is little trace of those developments outside of mathematical logic and model theory. But it seems fair to say that there is a widespread conviction that the principles embodied in the Zermelo - Fraenkel theory with Choice (ZFC) are a correct description of the set theoretic underpinnings of mathematics. In most textbooks of the kind referred to above, there is, of course, no discussion of these matters, and set theory is assumed informally, although more advanced principles like Choice or sometimes Replacement are often mentioned explicitly. This implicitly fixes a point of view of the mathemat ical universe which is at odds with the results in foundations. For example most mathematicians still take it for granted that the real number system is uniquely determined up to isomorphism, which is a correct point of view as long as one does not accept to look at "unnatural" interpretations of the membership relation Mathematics Global analysis (Mathematics) Logic, Symbolic and mathematical Analysis Mathematical Logic and Foundations Mathematik Nonstandard-Analysis (DE-588)4137021-1 gnd rswk-swf Axiomatik (DE-588)4004038-0 gnd rswk-swf Nonstandard-Analysis (DE-588)4137021-1 s Axiomatik (DE-588)4004038-0 s 1\p DE-604 Reeken, Michael Sonstige oth https://doi.org/10.1007/978-3-662-08998-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kanovei, Vladimir Nonstandard Analysis, Axiomatically Mathematics Global analysis (Mathematics) Logic, Symbolic and mathematical Analysis Mathematical Logic and Foundations Mathematik Nonstandard-Analysis (DE-588)4137021-1 gnd Axiomatik (DE-588)4004038-0 gnd |
| subject_GND | (DE-588)4137021-1 (DE-588)4004038-0 |
| title | Nonstandard Analysis, Axiomatically |
| title_auth | Nonstandard Analysis, Axiomatically |
| title_exact_search | Nonstandard Analysis, Axiomatically |
| title_full | Nonstandard Analysis, Axiomatically by Vladimir Kanovei, Michael Reeken |
| title_fullStr | Nonstandard Analysis, Axiomatically by Vladimir Kanovei, Michael Reeken |
| title_full_unstemmed | Nonstandard Analysis, Axiomatically by Vladimir Kanovei, Michael Reeken |
| title_short | Nonstandard Analysis, Axiomatically |
| title_sort | nonstandard analysis axiomatically |
| topic | Mathematics Global analysis (Mathematics) Logic, Symbolic and mathematical Analysis Mathematical Logic and Foundations Mathematik Nonstandard-Analysis (DE-588)4137021-1 gnd Axiomatik (DE-588)4004038-0 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Logic, Symbolic and mathematical Analysis Mathematical Logic and Foundations Mathematik Nonstandard-Analysis Axiomatik |
| url | https://doi.org/10.1007/978-3-662-08998-9 |
| work_keys_str_mv | AT kanoveivladimir nonstandardanalysisaxiomatically AT reekenmichael nonstandardanalysisaxiomatically |