Realizability, Volume 152

1st Edition

An Introduction to its Categorical Side

Print ISBN: 9780444550200
eBook ISBN: 9780080560069
Imprint: Elsevier Science
Published Date: 6th March 2008
Page Count: 328
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Institutional Access


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 Material from previously unpublished sources such as Ph.D. theses, unpublished papers, etc.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.

Key Features

  • The first book to date on this subject area
  • Provides an clear introduction to Realizability with a comprehensive bibliography
  • Easy to read and mathematically rigorous
  • Written by an expert in the field


University libraries, PhD students and advanced undergraduates as well as professional logicians

Table of Contents


  1. Partial Combinatory Algebras
  2. Realizability triposes and toposes
  3. The effective topos
  4. Variations on Realizability


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© Elsevier Science 2008
Elsevier Science
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"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