English

Spectrum of FO logic with quantifier depth 4 is finite

Combinatorics 2024-01-17 v5

Abstract

The kk-spectrum is the set of all α>0\alpha>0 such that G(n,nα)G(n,n^{-\alpha}) does not obey the 0-1 law for FO sentences with quantifier depth at most kk. In this paper, we prove that the minimum kk such that the kk-spectrum is infinite equals 5.

Keywords

Cite

@article{arxiv.2111.11470,
  title  = {Spectrum of FO logic with quantifier depth 4 is finite},
  author = {Yury Yarovikov and Maksim Zhukovskii},
  journal= {arXiv preprint arXiv:2111.11470},
  year   = {2024}
}