The Star Height Hierarchy Vs. The Variable Hierarchy
Logic in Computer Science
2009-04-13 v1 Computer Science and Game Theory
Abstract
The star height hierarchy (resp. the variable hierarchy) results in classifying -terms into classes according to the nested depth of fixed point operators (resp. to the number of bound variables). We prove, under some assumptions, that the variable hierarchy is a proper refinement of the star height hierarchy. We mean that the non collapse of the variable hierarchy implies the non collapse of the star height hierarchy. The proof relies on the combinatorial characterization of the two hierarchies.
Cite
@article{arxiv.0904.1701,
title = {The Star Height Hierarchy Vs. The Variable Hierarchy},
author = {Walid Belkhir},
journal= {arXiv preprint arXiv:0904.1701},
year = {2009}
}