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The Relation Reflection Scheme

✍ Scribed by Peter Aczel

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
115 KB
Volume
54
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

We introduce a new axiom scheme for constructive set theory, the Relation Reflection Scheme (RRS). Each instance of this scheme is a theorem of the classical set theory ZF. In the constructive set theory CZF^–^, when the axiom scheme is combined with the axiom of Dependent Choices (DC), the result is equivalent to the scheme of Relative Dependent Choices (RDC). In contrast to RDC, the scheme RRS is preserved in Heyting‐valued models of CZF^–^ using set‐generated frames. We give an application of the scheme to coinductive definitions of classes. (Β© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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