Abstract
A k-spectrum is a set of all positive α such that the random binomial graph \(G(n,{{n}^{{ - \alpha }}})\) does not obey the zero–one law for first-order formulas with a quantifier depth at most k. We have proved that the minimal k such that the k-spectrum is infinite equals 5.
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This work was supported by the Russian Foundation for Basic Research, project no. 20-31-70025.
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Translated by I. Ruzanova
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Zhukovskii, M.E., Matushkin, A.D. & Yarovikov, Y.N. On the 4-Spectrum of First-Order Properties of Random Graphs. Dokl. Math. 104, 247–249 (2021). https://doi.org/10.1134/S1064562421050185
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DOI: https://doi.org/10.1134/S1064562421050185