Abstract
In this chapter we will present model constructions, or otherwise expressed, “concrete” realizability interpretations, for constructive set theories (sub-theories of intuitionistic ZF), patterned after the models of EM 0 and ML 1 given in preceding chapters. These models are of interest for two distinct reasons:
-
(i)
They sharpen our conception of the notion of “set” described in constructive set theory by giving specific and concrete examples of the kind of universe to which these theories can apply.
-
(ii)
They (or rather their formalized versions) provide interpretations of constructive set theory in various other theories, such as EM0, ML1, or subsystems of analysis, which help to clarify the relations between these different theories, both in terms of the notion of set described and in terms of the formal proof-theoretic strength of the theories.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Beeson, M.J. (1985). Constructive Models of Set Theory. In: Foundations of Constructive Mathematics. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-68952-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-68952-9_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-68954-3
Online ISBN: 978-3-642-68952-9
eBook Packages: Springer Book Archive