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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...
| Other Authors: | |
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| Format: | Printed Book |
| Language: | English |
| Series: | Lecture notes in logic ;
41. |
| Subjects: |
| LEADER | 03331cam a2200361 i 4500 | ||
|---|---|---|---|
| 008 | 140501s2013 enk b 000 0 eng c | ||
| 010 | |a 2013388711 | ||
| 020 | |a 1107014514 (Hardback) | ||
| 020 | |a 9781107014510 (Hardback) | ||
| 035 | |a (OCoLC)ocn865065496 | ||
| 042 | |a pcc | ||
| 084 | |2 msc |a 03C57 | ||
| 245 | 0 | 0 | |a Effective mathematics of the uncountable / |c 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. |
| 300 | |a viii, 197 pages ; |c 24 cm. | ||
| 490 | 1 | |a Lecture notes in logic ; |v 41 | |
| 500 | |a Symbols for "omega" and "Sigma" appear on source of information. | ||
| 504 | |a Includes bibliographical references. | ||
| 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. | |
| 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 | 0 | |a Computable functions. | |
| 650 | 0 | |a Model theory. | |
| 700 | 1 | |a Greenberg, Noam, |e editor of compilation. | |
| 700 | 1 | |a Hamkins, Joel David, |e editor of compilation. | |
| 700 | 1 | |a Hirschfeldt, Denis Roman, |e editor of compilation. | |
| 700 | 1 | |a Miller, Russell |e editor of compilation. | |
| 700 | 1 | 2 | |a Calvert, Wesley Crain. |
| 710 | 2 | |a Association for Symbolic Logic, |e issuing body. | |
| 830 | 0 | |a Lecture notes in logic ; |v 41. | |
| 906 | |a 7 |b cbc |c pccadap |d 2 |e ncip |f 20 |g y-gencatlg | ||
| 942 | |c BK | ||
| 955 | |b rl46 2014-05-01 z-processor |i rl02 2014-05-23 to Dewey |a rl11 2014-06-24 (rev) |a rl02 2014-08-01 discard copy 2 | ||
| 999 | |c 135850 |d 135850 | ||
| 952 | |0 0 |1 0 |4 0 |6 03C_GRE |7 0 |9 150391 |a MAT |b MAT |c ST1 |d 2015-04-30 |i 6733 |l 0 |o 03C GRE |p MAT6733 |r 2015-04-30 |w 2015-04-30 |y BK | ||