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Abstract
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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
such
that
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
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Mathematical Subject Classification 2010
Primary: 05C80
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Milestones
Received: 4 December 2019
Revised: 4 May 2020
Accepted: 28 May 2020
Published: 15 October 2020
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