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Zero-one laws for random graphs with vertices in a Boolean cube

Abstract

We study the limit probabilities of first-order properties for random graphs with vertices in a Boolean cube. We find sufficient conditions for a sequence of random graphs to obey the zero-one law for first-order formulas of bounded quantifier depth. We also find conditions implying a weakened version of the zero-one law.

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Correspondence to S. N. Popova.

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Original Russian Text © S.N. Popova, 2016, published in Matematicheskie Trudy, 2016, Vol. 19, No. 1, pp. 106–177.

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Popova, S.N. Zero-one laws for random graphs with vertices in a Boolean cube. Sib. Adv. Math. 27, 26–75 (2017). https://doi.org/10.3103/S1055134417010035

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Keywords

  • random graphs
  • zero-one laws
  • distance graphs