02478nam a22003858a 4500 CR9781139028592 UkCbUP 20171019114425.0 m|||||o||d|||||||| cr|||||||||||| 110221s2013||||enk s ||1 0|eng|d 9781139028592 (ebook) 9781107014510 (hardback) UkCbUP UkCbUP rda QA9.7 .E34 2013 n/a n/a Effective Mathematics of the Uncountable / Edited by Noam Greenberg, Denis Hirschfeldt, Joel David Hamkins, Russell Miller. Cambridge : Cambridge University Press, 2013. 1 online resource (204 pages) : digital, PDF file(s). text txt rdacontent computer c rdamedia online resource cr rdacarrier Lecture Notes in Logic ; no. 41 Title from publisher's bibliographic system (viewed on 09 Oct 2015). 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, editor of compilation. Hirschfeldt, Denis, editor of compilation. Hamkins, Joel David, editor of compilation. Miller, Russell, editor of compilation. Print version: 9781107014510 Lecture Notes in Logic ; no. 41. http://dx.doi.org/10.1017/CBO9781139028592 225532 225532