Effective Mathematics of the Uncountable (Lecture Notes in Logic, Series Number 41) - Hardcover

Hardcover

ISBN 10: 1107014514 ISBN 13: 9781107014510

Publisher: Cambridge University Press, 2013

Synopsis

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.

About this title

About the Authors

Noam Greenberg is a Rutherford Discovery Fellow of the Royal Society of New Zealand where his research interests include computability theory, algorithmic randomness, reverse mathematics, higher recursion theory, computable model theory and set theory.

Denis Hirschfeldt is a Professor of Mathematics at the University of Chicago and has previously held visiting positions at the University of Wisconsin, Madison and the University of Notre Dame. He was a recipient of the 2010 Sacks Prize of the Association for Symbolic Logic for expository writing.

Joel David Hamkins is a professor at the City University of New York and has held visiting positions at the University of California, Berkeley, Kobe University, Carnegie Mellon University, the University of Muenster, the University of Amsterdam and New York University.

Russell Miller holds an appointment as Professor of Mathematics jointly between Queens College and the CUNY Graduate Center. His research applies computability to other areas of mathematics, including model theory, set theory, commutative algebra, differential algebra, graph theory and topology.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2013
• Language: English
• ISBN 10: 1107014514
• ISBN 13: 9781107014510
• Binding: Hardcover
• Edition number: 1
• Number of pages: 204
• Editor: Greenberg Noam, Hirschfeldt Denis, Hamkins Joel David, Miller Russell