Constructive Zermelo-Fraenkel set theory and the limited principle of omniscience

Michael Rathjen

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arXiv · 1302.3037

Constructive Zermelo-Fraenkel set theory and the limited principle of omniscience

Michael Rathjen

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Abstract

In recent years the question of whether adding the limited principle of omniscience, LPO, to constructive Zermelo-Fraenkel set theory, CZF, increases its strength has arisen several times. As the addition of excluded middle for atomic formulae to CZF results in a rather strong theory, i.e. much stronger than classical Zermelo set theory, it is not obvious that its augmentation by LPO would be proof-theoretically benign. The purpose of this paper is to show that CZF +RDC+ LPO has indeed the same strength as CZF, where RDC stands for relativized dependent choice. In particular, these theories prove the same Pi-?0-2 theorems of arithmetic.

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Michael Rathjen. 2013-02-13. Constructive Zermelo-Fraenkel set theory and the limited principle of omniscience. https://arxiv.org/abs/1302.3037

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