You are accessing PhilPapers from Open University (UK), an institution that is not subscribed to PhilPapers. Starting on July 1, 2014, we ask institutions that grant philosophy degrees and are based in high-GDP countries to contribute to PhilPapers' maintenance and development through a subscription. See this page for details. Please show your support by contacting your librarian.

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)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 10,350
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Citations of this work BETA
Andrew W. Swan (2014). CZF Does Not Have the Existence Property. Annals of Pure and Applied Logic 165 (5):1115-1147.
Albert Ziegler (2010). Refinement is Equivalent to Fullness. Mathematical Logic Quarterly 56 (6):666-669.
Giovanni Curi (2012). Topological Inductive Definitions. Annals of Pure and Applied Logic 163 (11):1471-1483.
Robert S. Lubarsky (2012). Topological Forcing Semantics with Settling. Annals of Pure and Applied Logic 163 (7):820-830.
Similar books and articles
Arnold W. Miller (1983). Mapping a Set of Reals Onto the Reals. Journal of Symbolic Logic 48 (3):575-584.
Johanna N. Y. Franklin (2010). Subclasses of the Weakly Random Reals. Notre Dame Journal of Formal Logic 51 (4):417-426.
Janusz Pawlikowski (2001). Cohen Reals From Small Forcings. Journal of Symbolic Logic 66 (1):318-324.
George Barmpalias (2010). Relative Randomness and Cardinality. Notre Dame Journal of Formal Logic 51 (2):195-205.
John L. Bell (1999). Frege's Theorem in a Constructive Setting. Journal of Symbolic Logic 64 (2):486-488.
Analytics

Monthly downloads

Added to index

2010-08-24

Total downloads

5 ( #219,641 of 1,096,707 )

Recent downloads (6 months)

1 ( #271,187 of 1,096,707 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.