Effective mathematics of the uncountable
- Cambridge : Cambridge University Press, 2013.
- Copyright notice
- Physical description
- viii, 197 pages ; 24 cm.
- Lecture notes in logic ; 41.
QA9.7 .E344 2013
- Unknown QA9.7 .E344 2013
- Includes bibliographical references.
- 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 R-computable structures W. Calvert and J. E. Porter-- 5. Effective model theory via the SIGMA-definability approach Alexey Stukachev-- 6. Computable structure theory using admissible recursion theory on omega1 Noam Greenberg and Julia F. Knight-- 7. E-recursive 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; 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.
(source: Nielsen Book Data)
- Publication date
- Copyright date
- 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).
- Lecture notes in logic ; 41
- "Lecture notes in logic: a publication for The Association for Symbolic Logic."--Page ii.