LEADER 04087nam 22007092 450 001 9910464679303321 005 20160422133626.0 010 $a1-139-89203-7 010 $a1-107-50349-3 010 $a1-139-02859-6 010 $a1-107-51647-1 010 $a1-107-01451-4 010 $a1-107-51376-6 010 $a1-107-49634-9 010 $a1-107-50615-8 035 $a(CKB)3460000000129043 035 $a(EBL)1543609 035 $a(OCoLC)866440808 035 $a(SSID)ssj0001156938 035 $a(PQKBManifestationID)11632212 035 $a(PQKBTitleCode)TC0001156938 035 $a(PQKBWorkID)11201117 035 $a(PQKB)10990912 035 $a(UkCbUP)CR9781139028592 035 $a(MiAaPQ)EBC1543609 035 $a(Au-PeEL)EBL1543609 035 $a(CaPaEBR)ebr10812152 035 $a(CaONFJC)MIL552441 035 $a(EXLCZ)993460000000129043 100 $a20110221d2013|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aEffective mathematics of the uncountable /$fedited by Noam Greenberg, Victoria University of Wellington, Joel David Hamkins, City University of New York, Denis Hirschfeldt, University of Chicago, Russell Miller, City University of New York$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2013. 215 $a1 online resource (viii, 197 pages) $cdigital, PDF file(s) 225 1 $aLecture notes in logic ;$v41 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a1-306-21190-5 311 $a1-107-52118-1 320 $aIncludes bibliographical references. 327 $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 Montalba?n and Andre? Nies -- E-recursive intuitions / Gerald E. Sacks -- Reverse mathematics, countable and uncountable : a computational approach -- Effective model theory : an approach via [Sigma]-definability. 330 $aClassical computable model theory is most naturally concerned with countable domains. There are, however, several methods - some old, some new - that have extended its basic concepts to uncountable structures. Unlike in the classical case, however, no single dominant approach has emerged, and different methods reveal different aspects of the computable content of uncountable mathematics. This book contains introductions to eight major approaches to computable uncountable mathematics: descriptive set theory; infinite time Turing machines; Blum-Shub-Smale computability; Sigma-definability; computability theory on admissible ordinals; E-recursion theory; local computability; and uncountable reverse mathematics. This book provides an authoritative and multifaceted introduction to this exciting new area of research that is still in its early stages. It is ideal as both an introductory text for graduate and advanced undergraduate students and a source of interesting new approaches for researchers in computability theory and related areas. 410 0$aLecture notes in logic ;$v41. 606 $aModel theory 606 $aComputable functions 615 0$aModel theory. 615 0$aComputable functions. 676 $a511.3/4 702 $aGreenberg$b Noam$f1974- 702 $aHamkins$b Joel David 702 $aHirschfeldt$b Denis Roman 702 $aMiller$b Russell$c(Professor of mathematics), 712 02$aAssociation for Symbolic Logic, 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910464679303321 996 $aEffective mathematics of the uncountable$92464116 997 $aUNINA