On the constructive Dedekind reals

Logic and Analysis 1 (2):131-152 (2008)
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
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/s11813-007-0005-6
Options
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 30,122
Through your library
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.

Add more references

Citations of this work BETA
Topological Inductive Definitions.Giovanni Curi - 2012 - Annals of Pure and Applied Logic 163 (11):1471-1483.
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.
CZF Does Not Have the Existence Property.Andrew W. Swan - 2014 - Annals of Pure and Applied Logic 165 (5):1115-1147.

View all 7 citations / Add more citations

Similar books and articles
On Constructing Completions.Laura Crosilla, Hajime Ishihara & Peter Schuster - 2005 - Journal of Symbolic Logic 70 (3):969-978.
Mapping a Set of Reals Onto the Reals.Arnold W. Miller - 1983 - Journal of Symbolic Logic 48 (3):575-584.
Subclasses of the Weakly Random Reals.Johanna N. Y. Franklin - 2010 - Notre Dame Journal of Formal Logic 51 (4):417-426.
Relative Randomness and Real Closed Fields.Alexander Raichev - 2005 - Journal of Symbolic Logic 70 (1):319 - 330.
Cohen Reals From Small Forcings.Janusz Pawlikowski - 2001 - Journal of Symbolic Logic 66 (1):318-324.
Relative Randomness and Cardinality.George Barmpalias - 2010 - Notre Dame Journal of Formal Logic 51 (2):195-205.
Frege's Theorem in a Constructive Setting.John L. Bell - 1999 - Journal of Symbolic Logic 64 (2):486-488.
On Non-Wellfounded Iterations of the Perfect Set Forcing.Vladimir Kanovei - 1999 - Journal of Symbolic Logic 64 (2):551-574.
Added to PP index
2010-08-24

Total downloads
13 ( #361,879 of 2,191,293 )

Recent downloads (6 months)
1 ( #291,146 of 2,191,293 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature