000			03339nam a22004098i 4500
001			CR9781139028592
003			UkCbUP
005			20200124160231.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			110221s2013||||enk o ||1 0|eng|d
020			_a9781139028592 (ebook)
020			_z9781107014510 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA9.7 _b.E34 2013
082	0	4	_a511.3/4 _223
245	0	0	_aEffective mathematics of the uncountable / _cedited 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.
264		1	_aCambridge : _bCambridge University Press, _c2013.
300			_a1 online resource (viii, 197 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aLecture notes in logic ; _v41
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aSome 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			_aClassical 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	_aModel theory.
650		0	_aComputable functions.
700	1		_aGreenberg, Noam, _d1974- _eeditor.
700	1		_aHamkins, Joel David, _eeditor.
700	1		_aHirschfeldt, Denis Roman, _eeditor.
700	1		_aMiller, Russell _c(Professor of mathematics), _eeditor.
710	2		_aAssociation for Symbolic Logic, _eissuing body.
776	0	8	_iPrint version: _z9781107014510
830		0	_aLecture notes in logic ; _v41.
856	4	0	_uhttps://doi.org/10.1017/CBO9781139028592
999			_c517654 _d517652