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On limit points of spectra of the random graph first-order properties

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Abstract

New bounds on the minimum and maximum limit points of spectra of first-order properties of the Erdös–Rényi random graph are obtained. These results are used to improve bounds on the minimal quantifier depths of first-order formulas with infinite spectra. Moreover, we prove that there are no limit points of the spectra in the interval (1–21–k, 1).

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

    M. E. Zhukovskii

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  1. M. E. Zhukovskii
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Correspondence to M. E. Zhukovskii.

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Original Russian Text © M.E. Zhukovskii, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 4, pp. 403–406.

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Zhukovskii, M.E. On limit points of spectra of the random graph first-order properties. Dokl. Math. 92, 719–722 (2015). https://doi.org/10.1134/S1064562415060265

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  • DOI: https://doi.org/10.1134/S1064562415060265

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