Effective mathematics of the uncountable
 Language
 English.
 Publication
 Cambridge : Cambridge University Press, 2013.
 Copyright notice
 ©2013
 Physical description
 viii, 197 pages ; 24 cm.
 Series
 Lecture notes in logic ; 41.
Access
Available online

Stacks

Unknown
QA9.7 .E344 2013

Unknown
QA9.7 .E344 2013
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Contributors
 Contributor
 Greenberg, Noam, 1974 editor of compilation.
 Hamkins, Joel David, editor of compilation.
 Hirschfeldt, Denis Roman editor of compilation.
 Miller, Russell (Professor of mathematics), editor of compilation.
 Association for Symbolic Logic, issuing body.
Contents/Summary
 Bibliography
 Includes bibliographical references.
 Contents

 List of contributors Preface 1. Introduction 2. Borel structures: a brief survey Antonio Montalban and Andre Nies 3. Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals Samuel Coskey and Joel David Hamkins 4. Some results on Rcomputable structures W. Calvert and J. E. Porter 5. Effective model theory via the SIGMAdefinability approach Alexey Stukachev 6. Computable structure theory using admissible recursion theory on omega1 Noam Greenberg and Julia F. Knight 7. Erecursive intuitions Gerald E. Sacks 8. Local computability and uncountable structures Russell Miller 9. Reverse mathematics, countable and uncountable: a computational approach Richard A. Shore.
 (source: Nielsen Book Data)
 Publisher's 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; BlumShubSmale computability; Sigmadefinability; computability theory on admissible ordinals; Erecursion 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Copyright date
 2013
 Responsibility
 edited 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).
 Series
 Lecture notes in logic ; 41
 Note
 "Lecture notes in logic: a publication for The Association for Symbolic Logic."Page ii.
 ISBN
 9781107014510 (hardcover)
 1107014514 (hardcover)