Vol. 9, No. 3, 2020

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On limit points of spectra of first-order sentences with quantifier depth 4

Yury Yarovikov

Vol. 9 (2020), No. 3, 303–331
Abstract

We study the asymptotic behavior of probabilities of first-order properties of sparse binomial random graphs. We consider properties with quantifier depth not more than 4. It is known that the only possible limit points of the spectrum (i.e., the set of all positive α such that G(n,nα) does not obey the zero-one law with respect to the property) of such a property are 1/2 and 3/5. We prove that 1/2 is not a limit point of the spectrum.

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Keywords
random graphs, first-order logic, zero-one law
Mathematical Subject Classification 2010
Primary: 05C80
Milestones
Received: 4 December 2019
Revised: 4 May 2020
Accepted: 28 May 2020
Published: 15 October 2020
Authors
Yury Yarovikov
Moscow Institute of Physics and Technology
Moscow
Russia