Church's thesis, continuity, and set theory

Journal of Symbolic Logic 49 (2):630-643 (1984)
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
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DOI 10.2307/2274195
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References found in this work BETA
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 Pure and Applied Logic 23 (2):127.

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Citations of this work BETA
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.

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