A note on Bar Induction in Constructive Set Theory

Mathematical Logic Quarterly 52 (3):253-258 (2006)
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Abstract

Bar Induction occupies a central place in Brouwerian mathematics. This note is concerned with the strength of Bar Induction on the basis of Constructive Zermelo-Fraenkel Set Theory, CZF. It is shown that CZF augmented by decidable Bar Induction proves the 1-consistency of CZF. This answers a question of P. Aczel who used Bar Induction to give a proof of the Lusin Separation Theorem in the constructive set theory CZF

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Michael Rathjen
University of Leeds

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References found in this work

Constructive set theory.John Myhill - 1975 - Journal of Symbolic Logic 40 (3):347-382.
The foundations of intuitionistic mathematics.Stephen Cole Kleene - 1965 - Amsterdam,: North-Holland Pub. Co.. Edited by Richard Eugene Vesley.
The strength of some Martin-Löf type theories.Edward Griffor & Michael Rathjen - 1994 - Archive for Mathematical Logic 33 (5):347-385.
Inaccessible set axioms may have little consistency strength.L. Crosilla & M. Rathjen - 2002 - Annals of Pure and Applied Logic 115 (1-3):33-70.

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