Realizability - An Introduction to Its Categorical Side

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

List of contents

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

Report

"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 Hyland's 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 Pitts's 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

Product details

• Authors: Jaap van Oosten, Jaap van Oosten, Jaap van Oosten, Jaap (Utrecht University van Oosten
• Publisher: ELSEVIER SCIENCE BV
• Languages: English
• Product format: Hardback
• Released: 06.03.2008
• EAN: 9780444515841
• ISBN: 978-0-444-51584-1
• No. of pages: 328
• Dimensions: 159 mm x 229 mm x 25 mm
• Series: Studies in Logic and the Found; Studies in Logic and the Foundations of Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Medicine > Non-clinical medicine; MEDICAL / Neurology, Neurology & clinical neurophysiology, Neurology and clinical neurophysiology