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arXiv · 1701.06517

First order sentences about random graphs: small number of alternations

Aleksandr Matushkin·Maksim Zhukovskii
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Abstract

Spectrum of a first order sentence is the set of all $α$ such that $G(n, n^{-α})$ does not obey zero-one law w.r.t. this sentence. We have proved that the minimal number of quantifier alternations of a first order sentence with an infinite spectrum equals 3. We have also proved that the spectrum of a first order sentence with a quantifier depth 4 has no limit points except possibly the points 1/2 and 3/5.

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Aleksandr Matushkin, Maksim Zhukovskii. 2017-09-26. First order sentences about random graphs: small number of alternations. https://arxiv.org/abs/1701.06517

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