@aeu_research

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

. (2013)cite arxiv:1302.3037Comment: 11 pages.

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.

Description

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

Links and resources

URL:
BibTeX key:
rathjen2013constructive
search on:

Comments and Reviews  
(0)

There is no review or comment yet. You can write one!

Tags


Cite this publication