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The Relation Reflection Scheme Peter Aczel

Summary: The Relation Reflection Scheme
Peter Aczel
Schools of Mathematics and Computer Science
The University of Manchester
September 14, 2007
1 Introduction
In this paper we introduce a new axiom scheme, the Relation Reflection
Scheme (RRS), for constructive set theory. Constructive set theory is an
extensional set theoretical setting for constructive mathematics. A formal
system for constructive set theory was first introduced by Myhill in [8]. In
[1, 2, 3] I introduced a formal system CZF that is closely related to Myhill's
formal system and gave a natural interpretation of CZF and extensions of it
in Martin-Lof's constructive type theory, [7]. The axiom system CZF can be
formulated in the same first order language as that of ZF, but uses intuition-
istic logic rather than classical logic. But when the law of excluded middle is
added the resulting classical theory has the same theorems as ZF. So, from
the classical point of view, CZF does not involve any choice principle. The
axiom CC of countable choice and even the stronger axiom DC of dependent
choices have been accepted principles of constructive mathematics that have


Source: Aczel, Peter - Departments of Mathematics & Computer Science, University of Manchester


Collections: Mathematics