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...

Full description

Saved in:
Bibliographic Details
Published inDoklady. Mathematics Vol. 98; no. 3; pp. 638 - 640
Main Authors Zhukovskii, M. E., Popova, S. N.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.11.2018
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Sentences
Online AccessGet full text

Cover

More Information
Summary: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