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On the Constructive Dedekind Reals: Extended Abstract

  • Robert S. Lubarsky
  • Michael Rathjen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4514)

Abstract

In order to built 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, CZF with Subset Collection replaced by Exponentiation, in which the Cauchy reals form a set while the Dedekind reals constitute a proper class.

Keywords

Transition Function Ground Model Kripke Model Proper Class Elementary Embedding 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Robert S. Lubarsky
    • 1
  • Michael Rathjen
    • 2
  1. 1.Department of Mathematical Sciences, Florida Atlantic University 
  2. 2.Department of Pure Mathematics, University of Leeds 

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