%0 Generic %1 rathjen2013constructive %A Rathjen, Michael %D 2013 %K constructive fraenkel set theory zermelo %T Constructive Zermelo-Fraenkel set theory and the limited principle of omniscience %U http://arxiv.org/abs/1302.3037 %X 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.

@misc{rathjen2013constructive, 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.}, added-at = {2013-12-23T04:23:24.000+0100}, author = {Rathjen, Michael}, biburl = {https://www.bibsonomy.org/bibtex/25f23786a07284a436aad9a08225a4c4e/aeu_research}, description = {Constructive Zermelo-Fraenkel set theory and the limited principle of omniscience}, interhash = {3ebf737bfce1d42679b1f798e4ce9a6e}, intrahash = {5f23786a07284a436aad9a08225a4c4e}, keywords = {constructive fraenkel set theory zermelo}, note = {cite arxiv:1302.3037Comment: 11 pages}, timestamp = {2013-12-23T04:39:53.000+0100}, title = {Constructive Zermelo-Fraenkel set theory and the limited principle of omniscience}, url = {http://arxiv.org/abs/1302.3037}, year = 2013 }