Studia Logica 84 (3):361-368 (2006)

Authors
Laura Crosilla
University of Oslo
Abstract
Working in the weakening of constructive Zermelo-Fraenkel set theory in which the subset collection scheme is omitted, we show that the binary refinement principle implies all the instances of the exponentiation axiom in which the basis is a discrete set. In particular binary refinement implies that the class of detachable subsets of a set form a set. Binary refinement was originally extracted from the fullness axiom, an equivalent of subset collection, as a principle that was sufficient to prove that the Dedekind reals form a set. Here we show that the Cauchy reals also form a set. More generally, binary refinement ensures that one remains in the realm of sets when one starts from discrete sets and one applies the operations of exponentiation and binary product a finite number of times.
Keywords Philosophy   Computational Linguistics   Mathematical Logic and Foundations   Logic
Categories (categorize this paper)
Reprint years 2007
ISBN(s)
DOI 10.1007/s11225-006-9014-9
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 60,021
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.

Add more references

Citations of this work BETA

Refinement is Equivalent to Fullness.Albert Ziegler - 2010 - Mathematical Logic Quarterly 56 (6):666-669.

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.
A Predicative Completion of a Uniform Space.Josef Berger, Hajime Ishihara, Erik Palmgren & Peter Schuster - 2012 - Annals of Pure and Applied Logic 163 (8):975-980.
Pell Equations and Exponentiation in Fragments of Arithmetic.Paola D'Aquino - 1996 - Annals of Pure and Applied Logic 77 (1):1-34.
Discrete Subspaces of Countably Tight Compacta.I. Juhász & Z. Szentmiklóssy - 2006 - Annals of Pure and Applied Logic 140 (1):72-74.
A Note on the Axioms for Zilber’s Pseudo-Exponential Fields.Jonathan Kirby - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):509-520.
On the Constructive Dedekind Reals.Robert S. Lubarsky & Michael Rathjen - 2008 - Logic and Analysis 1 (2):131-152.

Analytics

Added to PP index
2009-01-28

Total views
124 ( #82,567 of 2,433,517 )

Recent downloads (6 months)
3 ( #217,362 of 2,433,517 )

How can I increase my downloads?

Downloads

My notes