| Description |
1 online resource (viii, 197 pages) : illustrations. |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
Lecture notes in logic ; 41
|
|
Lecture notes in logic ; 41.
|
| Bibliography |
Includes bibliographical references. |
| 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. |
| Summary |
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. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Model theory.
|
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Model theory. |
|
Computable functions.
|
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Computable functions. |
| Genre/Form |
Electronic books.
|
| Added Author |
Greenberg, Noam, 1974- editor, author.
|
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Hirschfeldt, Denis Roman, editor.
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Hamkins, Joel David, editor, author.
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Miller, Russell (Professor of mathematics), editor, author.
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| Other Form: |
Print version: Effective mathematics of the uncountable. Cambridge, United Kingdom : Cambridge University Press, 2013 9781107014510 (OCoLC)865065496 |
| ISBN |
9781139028592 (electronic book) |
|
1139028596 (electronic book) |
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9781461953678 (electronic book) |
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1461953677 (electronic book) |
|
9781107521186 |
|
1107521181 |
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9781107014510 (hardback) |
|
1107014514 (hardback) |
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9781306211901 |
|
1306211905 |
|
