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Realizability Jaap van Oosten (Utrecht University, The Netherlands)

Realizability By Jaap van Oosten (Utrecht University, The Netherlands)

Summary

Presents an introduction to the basic concepts of realizability, a field which has passed several successive phases of abstraction. This title includes a bibliography.

Realizability Summary

Realizability: An Introduction to its Categorical Side: Volume 152 by Jaap van Oosten (Utrecht University, The Netherlands)

Aimed at starting researchers in the field, Realizability gives a rigorous, yet reasonable introduction to the basic concepts of a field which has passed several successive phases of abstraction. Material from previously unpublished sources such as Ph.D. theses, unpublished papers, etc. has been molded into one comprehensive presentation of the subject area.

Realizability Reviews

"This book aims at beginning researchers in the field of realizability and so emphasizes technical tools rather than any overview of methods or results. The central object here which created the categorical approach to realizability is Martin Hylands effective topos called Eff. The author advises that readers interested in getting directly to that topos can skip Chapter 1 and will only need "some parts of Chapter 2" (p. xii). However, that opening material will be needed for any research career on this and other realizability toposes. The reader is assumed to know some amount of general category theory as well as to have an "acquaintance with the notion of a topos" (p. vi). The tools are presented very clearly and this is especially advantageous for the idea of a tripos. The standard reference on triposes has been Andrew Pittss 1982 Ph.D. dissertation [The theory of triposes. Cambridge: Univ. Cambridge (1982)]. Considerable simplification has been possible since that pioneering work. This book gives a very clear exposition and should become the reference." --Zentralblatt MATH 1225-1

Table of Contents

Introduction1. Partial Combinatory Algebras2. Realizability triposes and toposes3. The effective topos4. Variations on Realizability

Additional information

NPB9780444515841
9780444515841
0444515844
Realizability: An Introduction to its Categorical Side: Volume 152 by Jaap van Oosten (Utrecht University, The Netherlands)
New
Hardback
Elsevier Science & Technology
2008-03-06
328
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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Customer Reviews - Realizability