Greenberg, Noam editor of compilation. Hirschfeldt, Denis editor of compilation. Hamkins, Joel David editor of compilation. Miller, Russell editor of compilation. text enk 2013 monographic eng

electronic

1 online resource (204 pages) : digital, PDF file(s). 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. Edited by Noam Greenberg, Denis Hirschfeldt, Joel David Hamkins, Russell Miller. Title from publisher's bibliographic system (viewed on 09 Oct 2015). Model theory Computable functions QA9.7 .E34 2013 n/a 9781139028592 (ebook) http://dx.doi.org/10.1017/CBO9781139028592 http://dx.doi.org/10.1017/CBO9781139028592 UkCbUP 110221 20171019154626.0 CR9781139028592