Spectrum of FO Logic with Quantifier Depth 4 is Finite
Yury Yarovikov, Maksim Evgen'evich Zhukovskii · ACM Transactions on Computational Logic · 2024
The k -spectrum is the set of all α > 0 such that G(n,n −α ) does not obey the 0-1 law for FO sentences with quantifier depth at most k . In this article, we prove that the minimum k such that the k -spectrum is infinite equals 5.