First order sentences about random graphs: small number of alternations
Combinatorics
2017-09-27 v3
Abstract
Spectrum of a first order sentence is the set of all such that does not obey zero-one law w.r.t. this sentence. We have proved that the minimal number of quantifier alternations of a first order sentence with an infinite spectrum equals 3. We have also proved that the spectrum of a first order sentence with a quantifier depth 4 has no limit points except possibly the points 1/2 and 3/5.
Keywords
Cite
@article{arxiv.1701.06517,
title = {First order sentences about random graphs: small number of alternations},
author = {Aleksandr Matushkin and Maksim Zhukovskii},
journal= {arXiv preprint arXiv:1701.06517},
year = {2017}
}