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Regular version of the site

Article

Infinite spectra of first-order properties for random hypergraphs

Problems of Information Transmission. 2018. Vol. 54. No. 3. P. 281-289.

We study the asymptotic behavior of probabilities of first-order properties for random uniform hypergraphs. In 1990, J. Spencer introduced the notion of a spectrum for graph properties and proved the existence of a first-order property with an infinite spectrum. In this paper we give a definition of a spectrum for properties of uniform hypergraphs and establish an almost tight bound for the minimum quantifier depth of a first-order formula with infinite spectrum.