TY - BOOK ID - 67110004 TI - Effective mathematics of the uncountable AU - Greenberg, Noam AU - Hamkins, Joel David AU - Hirschfeldt, Denis Roman AU - Miller, Russell AU - Association for Symbolic Logic PY - 2013 VL - 41 SN - 9781107014510 9781139028592 1139028596 9781461953678 1461953677 9781107521186 1107521181 9781306211901 1306211905 1107014514 1139892037 1107503493 1107516471 1107513766 1107496349 1107506158 PB - Cambridge : Cambridge University Press, DB - UniCat KW - Computable functions. KW - Logic, Symbolic and mathematical. KW - Algebra of logic KW - Logic, Universal KW - Mathematical logic KW - Symbolic and mathematical logic KW - Symbolic logic KW - Mathematics KW - Algebra, Abstract KW - Metamathematics KW - Set theory KW - Syllogism KW - Computability theory KW - Functions, Computable KW - Partial recursive functions KW - Recursive functions, Partial KW - Constructive mathematics KW - Decidability (Mathematical logic) KW - Model theory. KW - Logic, Symbolic and mathematical UR - https://www.unicat.be/uniCat?func=search&query=sysid:67110004 AB - 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. ER -