Email this article A Disproof the Le Bars Conjecture about the Zero–One Law for Existential Monadic Second-Order Sentences
- Authors: Zhukovskii M.E.1,2, Popova S.N.1
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Affiliations:
- Moscow Institute of Physics and Technology (State University)
- Caucasus Mathematical Center
- Issue: Vol 98, No 3 (2018)
- Pages: 638-640
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225602
- DOI: https://doi.org/10.1134/S1064562418070311
- ID: 225602
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Abstract
The Le Bars conjecture (2001) states that the binomial random graph G(n, \(\frac{1}{2}\)) 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.
About the authors
M. E. Zhukovskii
Moscow Institute of Physics and Technology (State University); Caucasus Mathematical Center
Author for correspondence.
Email: zhukmax@gmail.com
Russian Federation, Dolgoprudnyi, Moscow oblast, 141700; Maikop, Maikop, Republic of Adygea, 385000
S. N. Popova
Moscow Institute of Physics and Technology (State University)
Email: zhukmax@gmail.com
Russian Federation, Dolgoprudnyi, Moscow oblast, 141700
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