The Relation Reflection Scheme

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


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



    Upload a copy of this work     Papers currently archived: 92,873

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

Non-deterministic inductive definitions.Benno van den Berg - 2013 - Archive for Mathematical Logic 52 (1-2):113-135.
Some coinductive graphs.A. H. Lachlan - 1990 - Archive for Mathematical Logic 29 (4):213-229.
Coinductive formulas and a many-sorted interpolation theorem.Ursula Gropp - 1988 - Journal of Symbolic Logic 53 (3):937-960.
Syntactic calculus with dependent types.Aarne Ranta - 1998 - Journal of Logic, Language and Information 7 (4):413-431.
Does reflection lead to wise choices?Lisa Bortolotti - 2011 - Philosophical Explorations 14 (3):297-313.
James sequences and Dependent Choices.Marianne Morillon - 2005 - Mathematical Logic Quarterly 51 (2):171-186.
Dependent Choices and Anti-Foundation.Hisato Muraki - 2002 - Mathematical Logic Quarterly 48 (4):607-623.


Added to PP

26 (#627,957)

6 months
7 (#486,337)

Historical graph of downloads
How can I increase my downloads?

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.

Add more citations

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.

Add more references