Name
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 Π20 theorems of arithmetic. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1016/j.apal.2013.08.001 | Annals of Pure and Applied Logic |
Keywords | Field | DocType |
primary,secondary | Set theory,Law of excluded middle,Zermelo–Fraenkel set theory,Zermelo set theory,Constructive,Omniscience,Pure mathematics,Bar induction,Constructive set theory,Mathematics | Journal |
Volume | Issue | ISSN |
165 | 2 | 0168-0072 |
Citations | PageRank | References |
2 | 0.40 | 8 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael Rathjen | 1 | 42 | 6.58 |