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

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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.

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References

  1. M. E. Zhukovskii and A. M. Raigorodskii, Russ. Math. Surv. 70 (1), 33–81 (2015).

    Article  Google Scholar 

  2. S. Janson, T. Luczak, and A. Rucinski, Random Graphs (Wiley, New York, 2000).

    Book  MATH  Google Scholar 

  3. J. H. Spencer, The Strange Logic of Random Graphs (Springer, Berlin, 2001).

    Book  MATH  Google Scholar 

  4. N. K. Vereshchagin and A. Shen’, Languages and Calculi (MNTsMO, Moscow, 2000) [in Russian].

    Google Scholar 

  5. M. E. Zhukovskii and M. G. Sánchez, Dokl. Math. 96 (3), 598–600 (2017).

    Article  MathSciNet  Google Scholar 

  6. J.-M. Le Bars, Inf. Process. Lett. 77, 43–48 (2001).

    Article  Google Scholar 

  7. L. Libkin, Elements of Finite Model Theory (Springer, Berlin, 2004).

    Book  MATH  Google Scholar 

  8. Yu. V. Glebskii, D. I. Kogan, M. I. Legon’kii, and V. A. Talanov, Kibernetika 2, 17–27 (1969).

    Google Scholar 

  9. R. Fagin, J. Symbol. Logic 41, 50–58 (1976).

    Article  Google Scholar 

  10. M. E. Zhukovskii and A. E. Medvedeva, Math. Notes 99 (3), 362–367 (2016).

    Article  MathSciNet  Google Scholar 

  11. M. E. Zhukovskii and L. B. Ostrovskii, Izv. Math. 81 (6), 1155–1167 (2017).

    Article  MathSciNet  Google Scholar 

  12. A. D. Matushkin and M. E. Zhukovskii, Discrete Appl. Math. 236, 329–346 (2018).

    Article  MathSciNet  Google Scholar 

  13. M. Kaufmann and S. Shelah, Discrete Math. 54, 285–293 (1985).

    Article  MathSciNet  Google Scholar 

  14. M. Kaufmann, “Counterexample to the 0–1 law for existential monadic second-order logic,” Technical Report, CLI Internal Note 32, Computational Logic Inc., December, 1987.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow oblast, 141700, Russia

    M. E. Zhukovskii & S. N. Popova

  2. Caucasus Mathematical Center, Adyghe State University, Maikop, Maikop, Republic of Adygea, 385000, Russia

    M. E. Zhukovskii

Authors
  1. M. E. Zhukovskii
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  2. S. N. Popova
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Correspondence to M. E. Zhukovskii.

Additional information

Original Russian Text © M.E. Zhukovskii, S.N. Popova, 2018, published in Doklady Akademii Nauk, 2018, Vol. 483, No. 6.

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Zhukovskii, M.E., Popova, S.N. A Disproof the Le Bars Conjecture about the Zero–One Law for Existential Monadic Second-Order Sentences. Dokl. Math. 98, 638–640 (2018). https://doi.org/10.1134/S1064562418070311

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  • DOI: https://doi.org/10.1134/S1064562418070311

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