Problems of Information Transmission

, Volume 54, Issue 3, pp 281–289 | Cite as

Infinite Spectra of First-Order Properties for Random Hypergraphs

  • S. N. PopovaEmail author
Large Systems


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.


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© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Moscow Institute of Physics and Technology (State University)MoscowRussia

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