A Disproof the Le Bars Conjecture about the Zero–One Law for Existential Monadic Second-Order Sentences

A Disproof the Le Bars Conjecture about the Zero–One Law for Existential Monadic Second-Order Sentences

The Le Bars conjecture (2001) states that the binomial random graph G ( n , 1 2 ) obeys the zero–one law for existential monadic sentences with two first-order variables. This conjecture is disproved. Moreover, it is proved that there exists an existential monadic sentence with a single monadic vari...

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Veröffentlicht in:Doklady. Mathematics 2018-11, Vol.98 (3), p.638-640
Hauptverfasser: Zhukovskii, M. E., Popova, S. N.
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
Sentences
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Zusammenfassung:The Le Bars conjecture (2001) states that the binomial random graph G ( n , 1 2 ) obeys the zero–one law for existential monadic sentences with two first-order variables. This conjecture is disproved. Moreover, it is proved that there exists an existential monadic sentence with a single monadic variable and two first-order variables whose truth probability does not converge.
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562418070311