Iterating the recursively Mahlo operations
Logic
2010-05-13 v1
Abstract
In this paper we address a problem: How far can we iterate lower recursively Mahlo operations in higher reflecting universes? Or formally: How much can lower recursively Mahlo operations be iterated in set theories for higher reflecting universes? It turns out that in -reflecting universes the lowest recursively Mahlo operation can be iterated along towers of -exponential orderings of height , and that all we can do is such iterations. Namely the set theory for -reflecting universes is proof-theoretically reducible to iterations of the operation along such a tower.
Cite
@article{arxiv.1005.1987,
title = {Iterating the recursively Mahlo operations},
author = {Toshiyasu Arai},
journal= {arXiv preprint arXiv:1005.1987},
year = {2010}
}