Functional interpretations: from the dialectica interpretation to functional interpretations of analysis and set theory
"This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory. The subject goes back to Gödel's Dialectica interpretation of Heyting arithmetic which replaces nested quantification by higher type operations and thus reduces the consistency pro...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Publishing Company Pte Limited
2019
|
| Schlagworte: | |
| Online-Zugang: | UBY01 Volltext |
| Zusammenfassung: | "This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory. The subject goes back to Gödel's Dialectica interpretation of Heyting arithmetic which replaces nested quantification by higher type operations and thus reduces the consistency problem for arithmetic to the problem of computability of primitive recursive functionals of finite types. Regular functional interpretations, in particular the Dialectica interpretation and its generalization to finite types, the Diller-Nahm interpretation, are studied on Heyting as well as Peano arithmetic in finite types and extended to functional interpretations of constructive as well as classical systems of analysis and set theory. Kreisel's modified realization and Troelstra's hybrids of it are presented as interpretations of Heyting arithmetic and extended to constructive set theory, both in finite types. They serve as background for the construction of hybrids of the Diller-Nahm interpretation of Heyting arithmetic and constructive set theory, again in finite types. All these functional interpretations yield relative consistency results and closure under relevant rules of the theories in question as well as axiomatic characterizations of the functional translations."-- |
| Beschreibung: | Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader |
| Beschreibung: | 1 online resource (248 pages) illustrations |
| ISBN: | 9789814551403 |
Internformat
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| 505 | 8 | |a Includes bibliographical references and index | |
| 520 | |a "This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory. The subject goes back to Gödel's Dialectica interpretation of Heyting arithmetic which replaces nested quantification by higher type operations and thus reduces the consistency problem for arithmetic to the problem of computability of primitive recursive functionals of finite types. Regular functional interpretations, in particular the Dialectica interpretation and its generalization to finite types, the Diller-Nahm interpretation, are studied on Heyting as well as Peano arithmetic in finite types and extended to functional interpretations of constructive as well as classical systems of analysis and set theory. Kreisel's modified realization and Troelstra's hybrids of it are presented as interpretations of Heyting arithmetic and extended to constructive set theory, both in finite types. They serve as background for the construction of hybrids of the Diller-Nahm interpretation of Heyting arithmetic and constructive set theory, again in finite types. All these functional interpretations yield relative consistency results and closure under relevant rules of the theories in question as well as axiomatic characterizations of the functional translations."-- | ||
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Datensatz im Suchindex
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| author | Diller, Justus |
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| id | DE-604.BV046808865 |
| illustrated | Illustrated |
| index_date | 2024-07-03T14:58:22Z |
| indexdate | 2024-07-10T08:54:26Z |
| institution | BVB |
| isbn | 9789814551403 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032217467 |
| oclc_num | 1190674691 |
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| physical | 1 online resource (248 pages) illustrations |
| psigel | ZDB-124-WOP |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | World Scientific Publishing Company Pte Limited |
| record_format | marc |
| spelling | Diller, Justus Verfasser aut Functional interpretations from the dialectica interpretation to functional interpretations of analysis and set theory Justus Diller Singapore World Scientific Publishing Company Pte Limited 2019 1 online resource (248 pages) illustrations txt rdacontent c rdamedia cr rdacarrier Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references and index "This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory. The subject goes back to Gödel's Dialectica interpretation of Heyting arithmetic which replaces nested quantification by higher type operations and thus reduces the consistency problem for arithmetic to the problem of computability of primitive recursive functionals of finite types. Regular functional interpretations, in particular the Dialectica interpretation and its generalization to finite types, the Diller-Nahm interpretation, are studied on Heyting as well as Peano arithmetic in finite types and extended to functional interpretations of constructive as well as classical systems of analysis and set theory. Kreisel's modified realization and Troelstra's hybrids of it are presented as interpretations of Heyting arithmetic and extended to constructive set theory, both in finite types. They serve as background for the construction of hybrids of the Diller-Nahm interpretation of Heyting arithmetic and constructive set theory, again in finite types. All these functional interpretations yield relative consistency results and closure under relevant rules of the theories in question as well as axiomatic characterizations of the functional translations."-- Functional analysis Functionals Set theory Electronic books Erscheint auch als Druck-Ausgabe 9789814551397 https://www.worldscientific.com/worldscibooks/10.1142/8945 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Diller, Justus Functional interpretations from the dialectica interpretation to functional interpretations of analysis and set theory Includes bibliographical references and index Functional analysis Functionals Set theory |
| title | Functional interpretations from the dialectica interpretation to functional interpretations of analysis and set theory |
| title_auth | Functional interpretations from the dialectica interpretation to functional interpretations of analysis and set theory |
| title_exact_search | Functional interpretations from the dialectica interpretation to functional interpretations of analysis and set theory |
| title_exact_search_txtP | Functional interpretations from the dialectica interpretation to functional interpretations of analysis and set theory |
| title_full | Functional interpretations from the dialectica interpretation to functional interpretations of analysis and set theory Justus Diller |
| title_fullStr | Functional interpretations from the dialectica interpretation to functional interpretations of analysis and set theory Justus Diller |
| title_full_unstemmed | Functional interpretations from the dialectica interpretation to functional interpretations of analysis and set theory Justus Diller |
| title_short | Functional interpretations |
| title_sort | functional interpretations from the dialectica interpretation to functional interpretations of analysis and set theory |
| title_sub | from the dialectica interpretation to functional interpretations of analysis and set theory |
| topic | Functional analysis Functionals Set theory |
| topic_facet | Functional analysis Functionals Set theory |
| url | https://www.worldscientific.com/worldscibooks/10.1142/8945 |
| work_keys_str_mv | AT dillerjustus functionalinterpretationsfromthedialecticainterpretationtofunctionalinterpretationsofanalysisandsettheory |