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2020 On limit points of spectra of first-order sentences with quantifier depth 4
Yury Yarovikov
Mosc. J. Comb. Number Theory 9(3): 303-331 (2020). DOI: 10.2140/moscow.2020.9.303

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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Yury Yarovikov. "On limit points of spectra of first-order sentences with quantifier depth 4." Mosc. J. Comb. Number Theory 9 (3) 303 - 331, 2020. https://doi.org/10.2140/moscow.2020.9.303

Information

Received: 4 December 2019; Revised: 4 May 2020; Accepted: 28 May 2020; Published: 2020
First available in Project Euclid: 22 October 2020

zbMATH: 07272351
MathSciNet: MR4164871
Digital Object Identifier: 10.2140/moscow.2020.9.303

Subjects:
Primary: 05C80

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.9 • No. 3 • 2020
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