# The relation reflection schemeCitation formats

• Authors:
• Peter Aczel

## Standard

The relation reflection scheme. / Aczel, Peter.

Mathematical Logic Quarterly|Math. Logic Q.. Vol. 54 John Wiley & Sons Ltd, 2008. p. 5-11.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

## Harvard

Aczel, P 2008, The relation reflection scheme. in Mathematical Logic Quarterly|Math. Logic Q.. vol. 54, John Wiley & Sons Ltd, pp. 5-11, Workshop on Trends in Constructive Mathematics in Honor of the 60th Birthday of Douglas Bridges, Chiemsee Isl, GERMANY, 19/06/06. https://doi.org/10.1002/malq.200710035

## APA

Aczel, P. (2008). The relation reflection scheme. In Mathematical Logic Quarterly|Math. Logic Q. (Vol. 54, pp. 5-11). John Wiley & Sons Ltd. https://doi.org/10.1002/malq.200710035

## Vancouver

Aczel P. The relation reflection scheme. In Mathematical Logic Quarterly|Math. Logic Q.. Vol. 54. John Wiley & Sons Ltd. 2008. p. 5-11 https://doi.org/10.1002/malq.200710035

## Author

Aczel, Peter. / The relation reflection scheme. Mathematical Logic Quarterly|Math. Logic Q.. Vol. 54 John Wiley & Sons Ltd, 2008. pp. 5-11

## Bibtex

@inproceedings{2415a528e2254e47886a866664f9ab31,
title = "The relation reflection scheme",
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. {\circledC} 2008 Wiley-VCH Verlag GmbH & Co. KGaA.",
keywords = "Coinductive definitions, Constructive set theory, Dependent choices",
author = "Peter Aczel",
note = "Aczel, Peter 9 WEINHEIM 1 268AU",
year = "2008",
month = "2",
doi = "10.1002/malq.200710035",
language = "English",
volume = "54",
pages = "5--11",
booktitle = "Mathematical Logic Quarterly|Math. Logic Q.",
publisher = "John Wiley & Sons Ltd",

}

## RIS

TY - GEN

T1 - The relation reflection scheme

AU - Aczel, Peter

N1 - Aczel, Peter 9 WEINHEIM 1 268AU

PY - 2008/2

Y1 - 2008/2

N2 - 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. © 2008 Wiley-VCH Verlag GmbH & Co. KGaA.

AB - 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. © 2008 Wiley-VCH Verlag GmbH & Co. KGaA.

KW - Coinductive definitions

KW - Constructive set theory

KW - Dependent choices

U2 - 10.1002/malq.200710035

DO - 10.1002/malq.200710035

M3 - Conference contribution

VL - 54

SP - 5

EP - 11

BT - Mathematical Logic Quarterly|Math. Logic Q.

PB - John Wiley & Sons Ltd

ER -