Sinopsis
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.
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Acerca de los autores
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.
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Effective Mathematics of the Uncountable (Hardcover)
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Hardcover. Condición: new. Hardcover. 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. This book provides an authoritative and multifaceted introduction to eight major approaches to computation on uncountable mathematical domains. The perspectives explored within reveal different aspects of effective uncountable mathematics, making it an ideal resource for graduate and advanced undergraduate students and researchers in this exciting new area of study. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Nº de ref. del artículo: 9781107014510
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Effective Mathematics of the Uncountable (Hardcover)
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Hardcover. Condición: new. Hardcover. 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. This book provides an authoritative and multifaceted introduction to eight major approaches to computation on uncountable mathematical domains. The perspectives explored within reveal different aspects of effective uncountable mathematics, making it an ideal resource for graduate and advanced undergraduate students and researchers in this exciting new area of study. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Nº de ref. del artículo: 9781107014510
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Effective Mathematics of the Uncountable (Hardcover)
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Cambridge University Press, Cambridge, 2013
ISBN 10: 1107014514
ISBN 13: 9781107014510
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Hardcover. Condición: new. Hardcover. 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. This book provides an authoritative and multifaceted introduction to eight major approaches to computation on uncountable mathematical domains. The perspectives explored within reveal different aspects of effective uncountable mathematics, making it an ideal resource for graduate and advanced undergraduate students and researchers in this exciting new area of study. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Nº de ref. del artículo: 9781107014510
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