Effective mathematics of the uncountable /:
Classical computable model theory is most naturally concerned with countable domains. There are, however, several methods - some old, some new - that have extended its basic concepts to uncountable structures. Unlike in the classical case, however, no single dominant approach has emerged, and differ...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
[Ithaca, NY?] : Cambridge :
Association for Symbolic Logic ; Cambridge University Press,
2013.
|
| Schriftenreihe: | Lecture notes in logic ;
41. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Classical computable model theory is most naturally concerned with countable domains. There are, however, several methods - some old, some new - that have extended its basic concepts to uncountable structures. Unlike in the classical case, however, no single dominant approach has emerged, and different methods reveal different aspects of the computable content of uncountable mathematics. This book contains introductions to eight major approaches to computable uncountable mathematics: descriptive set theory; infinite time Turing machines; Blum-Shub-Smale computability; Sigma-definability; computability theory on admissible ordinals; E-recursion theory; local computability; and uncountable reverse mathematics. This book provides an authoritative and multifaceted introduction to this exciting new area of research that is still in its early stages. It is ideal as both an introductory text for graduate and advanced undergraduate students, and a source of interesting new approaches for researchers in computability theory and related areas.-- |
| Beschreibung: | 1 online resource (viii, 197 pages) : illustrations |
| Bibliographie: | Includes bibliographical references. |
| ISBN: | 9781139028592 1139028596 9781461953678 1461953677 9781107521186 1107521181 9781306211901 1306211905 |
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| 264 | 1 | |a [Ithaca, NY?] : |b Association for Symbolic Logic ; |a Cambridge : |b Cambridge University Press, |c 2013. | |
| 300 | |a 1 online resource (viii, 197 pages) : |b illustrations | ||
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| 505 | 0 | |a Some results on R-computable structures / Wesley Calvert and John E. Porter -- Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals / Samuel Coskey and Joel David Hamkins -- Computable structure theory using admissible recursion theory on [omega]1 using admissibility / Noam Greenberg and Julia F. Knight -- Local computability and uncountable structures / Russell Miller -- Borel structures : a brief survey / Antonio Montalbán and André Nies -- E-recursive intuitions / Gerald E. Sacks -- Reverse mathematics, countable and uncountable : a computational approach -- Effective model theory : an approach via [Sigma]-definability. | |
| 588 | 0 | |a Print version record. | |
| 520 | |a Classical computable model theory is most naturally concerned with countable domains. There are, however, several methods - some old, some new - that have extended its basic concepts to uncountable structures. Unlike in the classical case, however, no single dominant approach has emerged, and different methods reveal different aspects of the computable content of uncountable mathematics. This book contains introductions to eight major approaches to computable uncountable mathematics: descriptive set theory; infinite time Turing machines; Blum-Shub-Smale computability; Sigma-definability; computability theory on admissible ordinals; E-recursion theory; local computability; and uncountable reverse mathematics. This book provides an authoritative and multifaceted introduction to this exciting new area of research that is still in its early stages. It is ideal as both an introductory text for graduate and advanced undergraduate students, and a source of interesting new approaches for researchers in computability theory and related areas.-- |c Back cover. | ||
| 650 | 0 | |a Model theory. |0 http://id.loc.gov/authorities/subjects/sh85086421 | |
| 650 | 0 | |a Computable functions. |0 http://id.loc.gov/authorities/subjects/sh85029469 | |
| 650 | 6 | |a Théorie des modèles. | |
| 650 | 6 | |a Fonctions calculables. | |
| 650 | 7 | |a MATHEMATICS |x General. |2 bisacsh | |
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| 700 | 1 | |a Hirschfeldt, Denis Roman, |e editor. | |
| 700 | 1 | |a Hamkins, Joel David, |e editor, |e author. | |
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| author | Greenberg, Noam, 1974- Hamkins, Joel David Miller, Russell (Professor of mathematics) |
| author2 | Greenberg, Noam, 1974- Hirschfeldt, Denis Roman Hamkins, Joel David Miller, Russell (Professor of mathematics) |
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| author_facet | Greenberg, Noam, 1974- Hamkins, Joel David Miller, Russell (Professor of mathematics) Greenberg, Noam, 1974- Hirschfeldt, Denis Roman Hamkins, Joel David Miller, Russell (Professor of mathematics) |
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| contents | Some results on R-computable structures / Wesley Calvert and John E. Porter -- Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals / Samuel Coskey and Joel David Hamkins -- Computable structure theory using admissible recursion theory on [omega]1 using admissibility / Noam Greenberg and Julia F. Knight -- Local computability and uncountable structures / Russell Miller -- Borel structures : a brief survey / Antonio Montalbán and André Nies -- E-recursive intuitions / Gerald E. Sacks -- Reverse mathematics, countable and uncountable : a computational approach -- Effective model theory : an approach via [Sigma]-definability. |
| ctrlnum | (OCoLC)865081984 |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/4 |
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:40Z |
| institution | BVB |
| isbn | 9781139028592 1139028596 9781461953678 1461953677 9781107521186 1107521181 9781306211901 1306211905 |
| language | English |
| oclc_num | 865081984 |
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| physical | 1 online resource (viii, 197 pages) : illustrations |
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| publisher | Association for Symbolic Logic ; Cambridge University Press, |
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| series2 | Lecture notes in logic ; |
| spelling | Effective mathematics of the uncountable / edited by Noam Greenberg, Denis Hirschfeldt, Joel David Hamkins, Russell Miller. [Ithaca, NY?] : Association for Symbolic Logic ; Cambridge : Cambridge University Press, 2013. 1 online resource (viii, 197 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Lecture notes in logic ; 41 Includes bibliographical references. Some results on R-computable structures / Wesley Calvert and John E. Porter -- Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals / Samuel Coskey and Joel David Hamkins -- Computable structure theory using admissible recursion theory on [omega]1 using admissibility / Noam Greenberg and Julia F. Knight -- Local computability and uncountable structures / Russell Miller -- Borel structures : a brief survey / Antonio Montalbán and André Nies -- E-recursive intuitions / Gerald E. Sacks -- Reverse mathematics, countable and uncountable : a computational approach -- Effective model theory : an approach via [Sigma]-definability. Print version record. Classical computable model theory is most naturally concerned with countable domains. There are, however, several methods - some old, some new - that have extended its basic concepts to uncountable structures. Unlike in the classical case, however, no single dominant approach has emerged, and different methods reveal different aspects of the computable content of uncountable mathematics. This book contains introductions to eight major approaches to computable uncountable mathematics: descriptive set theory; infinite time Turing machines; Blum-Shub-Smale computability; Sigma-definability; computability theory on admissible ordinals; E-recursion theory; local computability; and uncountable reverse mathematics. This book provides an authoritative and multifaceted introduction to this exciting new area of research that is still in its early stages. It is ideal as both an introductory text for graduate and advanced undergraduate students, and a source of interesting new approaches for researchers in computability theory and related areas.-- Back cover. Model theory. http://id.loc.gov/authorities/subjects/sh85086421 Computable functions. http://id.loc.gov/authorities/subjects/sh85029469 Théorie des modèles. Fonctions calculables. MATHEMATICS General. bisacsh Funciones computables embne Teoría de modelos embne Computable functions fast Model theory fast Greenberg, Noam, 1974- editor, author. https://id.oclc.org/worldcat/entity/E39PCjGThJ8dVghVBHgHPDXQVP http://id.loc.gov/authorities/names/n2006002842 Hirschfeldt, Denis Roman, editor. Hamkins, Joel David, editor, author. Miller, Russell (Professor of mathematics), editor, author. https://id.oclc.org/worldcat/entity/E39PCjqD4J4cXjkRrc7k3TfkTb http://id.loc.gov/authorities/names/no2013134632 Print version: Effective mathematics of the uncountable. Cambridge, United Kingdom : Cambridge University Press, 2013 9781107014510 (OCoLC)865065496 Lecture notes in logic ; 41. http://id.loc.gov/authorities/names/n93082404 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=644567 Volltext |
| spellingShingle | Greenberg, Noam, 1974- Hamkins, Joel David Miller, Russell (Professor of mathematics) Effective mathematics of the uncountable / Lecture notes in logic ; Some results on R-computable structures / Wesley Calvert and John E. Porter -- Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals / Samuel Coskey and Joel David Hamkins -- Computable structure theory using admissible recursion theory on [omega]1 using admissibility / Noam Greenberg and Julia F. Knight -- Local computability and uncountable structures / Russell Miller -- Borel structures : a brief survey / Antonio Montalbán and André Nies -- E-recursive intuitions / Gerald E. Sacks -- Reverse mathematics, countable and uncountable : a computational approach -- Effective model theory : an approach via [Sigma]-definability. Model theory. http://id.loc.gov/authorities/subjects/sh85086421 Computable functions. http://id.loc.gov/authorities/subjects/sh85029469 Théorie des modèles. Fonctions calculables. MATHEMATICS General. bisacsh Funciones computables embne Teoría de modelos embne Computable functions fast Model theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85086421 http://id.loc.gov/authorities/subjects/sh85029469 |
| title | Effective mathematics of the uncountable / |
| title_auth | Effective mathematics of the uncountable / |
| title_exact_search | Effective mathematics of the uncountable / |
| title_full | Effective mathematics of the uncountable / edited by Noam Greenberg, Denis Hirschfeldt, Joel David Hamkins, Russell Miller. |
| title_fullStr | Effective mathematics of the uncountable / edited by Noam Greenberg, Denis Hirschfeldt, Joel David Hamkins, Russell Miller. |
| title_full_unstemmed | Effective mathematics of the uncountable / edited by Noam Greenberg, Denis Hirschfeldt, Joel David Hamkins, Russell Miller. |
| title_short | Effective mathematics of the uncountable / |
| title_sort | effective mathematics of the uncountable |
| topic | Model theory. http://id.loc.gov/authorities/subjects/sh85086421 Computable functions. http://id.loc.gov/authorities/subjects/sh85029469 Théorie des modèles. Fonctions calculables. MATHEMATICS General. bisacsh Funciones computables embne Teoría de modelos embne Computable functions fast Model theory fast |
| topic_facet | Model theory. Computable functions. Théorie des modèles. Fonctions calculables. MATHEMATICS General. Funciones computables Teoría de modelos Computable functions Model theory |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=644567 |
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