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\iteman{io-port 05998315}
\itemau{Zhukovskii, M.E.}
\itemti{Zero-one laws for first-order formulas with a bounded quantifier depth.}
\itemso{Dokl. Math. 83, No. 1, 8-11 (2011); translation from Dokl. Akad. Nauk 436, No. 1, 14-18 (2011).}
\itemab
Summary: This paper addresses the asymptotic behavior of probabilities of properties of random graphs in the Erd\H os-R\'enyi model $G(N, p)$. The properties are written in a first-order language with $p= N^{-\alpha}$, where $\alpha\in(0, 1)$. If $\alpha$ is rational, then the zero-one law in the usual sense does not hold for these graphs. We weaken the law by considering formulas with a quantifier depth bounded by a preset number. Due to this weakening, we are able to expand the set of $\alpha$s for which the new law holds and to give some examples disproving the new law for $\alpha$s that do not belong to this expanded set.
\itemrv{~}
\itemcc{}
\itemut{asymptotic behavior of probabilities of properties of random graphs}
\itemli{doi:10.1134/S1064562411010054}
\end