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:
| Weitere Verfasser: | , , , |
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| Format: | Elektronisch Tagungsbericht E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2013
|
| Schriftenreihe: | Lecture notes in logic
41 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers |
| 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: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (viii, 197 pages) |
| ISBN: | 9781139028592 |
| DOI: | 10.1017/CBO9781139028592 |
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| 505 | 8 | |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 | |
| 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 | ||
| 650 | 4 | |a Model theory | |
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| 700 | 1 | |a Hamkins, Joel David |4 edt | |
| 700 | 1 | |a Hirschfeldt, Denis Roman |4 edt | |
| 700 | 1 | |a Miller, Russell |4 edt | |
| 711 | 2 | |a Association for Symbolic Logic |a issuing body |j Sonstige |4 oth | |
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Datensatz im Suchindex
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| author2 | Greenberg, Noam 1974- Hamkins, Joel David Hirschfeldt, Denis Roman Miller, Russell |
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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 | (ZDB-20-CBO)CR9781139028592 (OCoLC)992848866 (DE-599)BVBBV043941512 |
| dewey-full | 511.3/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/4 |
| dewey-search | 511.3/4 |
| dewey-sort | 3511.3 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139028592 |
| format | Electronic Conference Proceeding eBook |
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| isbn | 9781139028592 |
| language | English |
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| spelling | Effective mathematics of the uncountable edited by Noam Greenberg, Victoria University of Wellington, Joel David Hamkins, City University of New York, Denis Hirschfeldt, University of Chicago, Russell Miller, City University of New York Cambridge Cambridge University Press 2013 1 online resource (viii, 197 pages) txt rdacontent c rdamedia cr rdacarrier Lecture notes in logic 41 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 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 Model theory Computable functions Greenberg, Noam 1974- edt Hamkins, Joel David edt Hirschfeldt, Denis Roman edt Miller, Russell edt Association for Symbolic Logic issuing body Sonstige oth Erscheint auch als Druckausgabe 978-1-107-01451-0 https://doi.org/10.1017/CBO9781139028592 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Effective mathematics of the uncountable 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 Computable functions |
| 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, Victoria University of Wellington, Joel David Hamkins, City University of New York, Denis Hirschfeldt, University of Chicago, Russell Miller, City University of New York |
| title_fullStr | Effective mathematics of the uncountable edited by Noam Greenberg, Victoria University of Wellington, Joel David Hamkins, City University of New York, Denis Hirschfeldt, University of Chicago, Russell Miller, City University of New York |
| title_full_unstemmed | Effective mathematics of the uncountable edited by Noam Greenberg, Victoria University of Wellington, Joel David Hamkins, City University of New York, Denis Hirschfeldt, University of Chicago, Russell Miller, City University of New York |
| title_short | Effective mathematics of the uncountable |
| title_sort | effective mathematics of the uncountable |
| topic | Model theory Computable functions |
| topic_facet | Model theory Computable functions |
| url | https://doi.org/10.1017/CBO9781139028592 |
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