Church's thesis, continuity, and set theory

Journal of Symbolic Logic 49 (2):630-643 (1984)
  Copy   BIBTEX

Abstract

Under the assumption that all "rules" are recursive (ECT) the statement $\operatorname{Cont}(N^N,N)$ that all functions from N N to N are continuous becomes equivalent to a statement KLS in the language of arithmetic about "effective operations". Our main result is that KLS is underivable in intuitionistic Zermelo-Fraenkel set theory + ECT. Similar results apply for functions from R to R and from 2 N to N. Such results were known for weaker theories, e.g. HA and HAS. We extend not only the theorem but the method, fp-realizability, to intuitionistic ZF

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,219

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Analytics

Added to PP
2009-01-28

Downloads
17 (#824,750)

6 months
3 (#928,914)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Effective inseparability in a topological setting.Dieter Spreen - 1996 - Annals of Pure and Applied Logic 80 (3):257-275.
Large sets in intuitionistic set theory.Harvey Friedman & Andrej Ščedrov - 1984 - Annals of Pure and Applied Logic 27 (1):1-24.
CZF does not have the existence property.Andrew W. Swan - 2014 - Annals of Pure and Applied Logic 165 (5):1115-1147.

Add more citations

References found in this work

Recursive models for constructive set theories.M. Beeson - 1982 - Annals of Mathematical Logic 23 (2-3):127-178.
Recursive models for constructive set theories.N. Beeson - 1982 - Annals of Mathematical Logic 23 (2/3):127.

Add more references