Bounded quantifier depth spectrum for random uniform hypegraphs
Combinatorics
2023-11-21 v1
Abstract
The notion of spectrum for first-order properties introduced by J. Spencer for Erdos-Renyi random graph is considered in relation to random uniform hypergraphs. In this work we study the set of limit points of the spectrum for first-order formulae with bounded quantifier depth and obtain bounds for its maximum value. Moreover, we prove zero-one k-laws for the random uniform hypergraph and improve the bounds for the maximum value of the spectrum for first-order formulae with bounded quantifier depth. We obtain that the maximum value of the spectrum belongs to some two-element set.
Keywords
Cite
@article{arxiv.2311.11168,
title = {Bounded quantifier depth spectrum for random uniform hypegraphs},
author = {Svetlana Popova},
journal= {arXiv preprint arXiv:2311.11168},
year = {2023}
}