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Title Effective mathematics of the uncountable / edited by Noam Greenberg, Denis Hirschfeldt, Joel David Hamkins, Russell Miller
Published [Ithaca, NY?] : Association for Symbolic Logic ; Cambridge : Cambridge University Press, 2013

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Description 1 online resource (viii, 197 pages) : illustrations
Series Lecture notes in logic ; 41
Lecture notes in logic ; 41.
Contents Some 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
Summary 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.-- Back cover
Bibliography Includes bibliographical references
Notes Print version record
Subject Model theory.
Computable functions.
MATHEMATICS -- General.
Funciones computables
Teoría de modelos
Computable functions
Model theory
Form Electronic book
Author Greenberg, Noam, 1974- editor, author.
Hirschfeldt, Denis Roman, editor
Hamkins, Joel David, editor, author
Miller, Russell (Professor of mathematics), editor, author.
ISBN 9781139028592
1139028596
9781461953678
1461953677
9781107521186
1107521181
9781306211901
1306211905