The Relation Reflection Scheme

Mathematical Logic Quarterly 54 (1):5-11 (2008)
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Abstract

We introduce a new axiom scheme for constructive set theory, the Relation Reflection Scheme . 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 , the result is equivalent to the scheme of Relative Dependent Choices . 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

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Citations of this work

A cumulative hierarchy of sets for constructive set theory.Albert Ziegler - 2014 - Mathematical Logic Quarterly 60 (1-2):21-30.
Abstract inductive and co-inductive definitions.Giovanni Curi - 2018 - Journal of Symbolic Logic 83 (2):598-616.

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References found in this work

Constructive set theory.John Myhill - 1975 - Journal of Symbolic Logic 40 (3):347-382.
Heyting-valued interpretations for constructive set theory.Nicola Gambino - 2006 - Annals of Pure and Applied Logic 137 (1-3):164-188.

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