Logic and Analysis 1 (2):131-152 (2008)

Authors
Michael Rathjen
University of Leeds
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
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DOI 10.1007/s11813-007-0005-6
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References found in this work BETA

Independence Results Around Constructive ZF.Robert S. Lubarsky - 2005 - Annals of Pure and Applied Logic 132 (2-3):209-225.
On Constructing Completions.Laura Crosilla, Hajime Ishihara & Peter Schuster - 2005 - Journal of Symbolic Logic 70 (3):969-978.
On the Cauchy Completeness of the Constructive Cauchy Reals.Robert S. Lubarsky - 2007 - Mathematical Logic Quarterly 53 (4‐5):396-414.

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Citations of this work BETA

Topological Inductive Definitions.Giovanni Curi - 2012 - Annals of Pure and Applied Logic 163 (11):1471-1483.
On the Cauchy Completeness of the Constructive Cauchy Reals.Robert S. Lubarsky - 2007 - Mathematical Logic Quarterly 53 (4‐5):396-414.
On the Existence of Stone-Čech Compactification.Giovanni Curi - 2010 - Journal of Symbolic Logic 75 (4):1137-1146.
Topological Forcing Semantics with Settling.Robert S. Lubarsky - 2012 - Annals of Pure and Applied Logic 163 (7):820-830.

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