Logic and Analysis

, Volume 1, Issue 2, pp 131–152 | Cite as

On the constructive Dedekind reals

Article

Abstract

In order to build the collection of Cauchy reals as a set in constructive set theory, the only power set-like principle needed is exponentiation. In contrast, the proof that the Dedekind reals form a set has seemed to require more than that. The main purpose here is to show that exponentiation alone does not suffice for the latter, by furnishing a Kripke model of constructive set theory, Constructive Zermelo–Fraenkel set theory with subset collection replaced by exponentiation, in which the Cauchy reals form a set while the Dedekind reals constitute a proper class.

Mathematics Subject Classification (2000)

03F50 03F55 03F60 03E35 03G30 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of Mathematical SciencesFlorida Atlantic UniversityBoca RatonUSA
  2. 2.Department of Pure MathematicsUniversity of LeedsLeedsUK

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