Logical laws for short existential monadic second-order sentences about graphs-Reference-Cited by-同舟云学术

Logical laws for short existential monadic second-order sentences about graphs

Published:2019-12-12 Issue:02 Volume:20 Page:2050007
ISSN:0219-0613
Container-title:Journal of Mathematical Logic
language:en
Short-container-title:J. Math. Log.

Author:

Zhukovskii M. E.¹²³

Affiliation:

1. Moscow Institute of Physics and Technology (National Research University), Laboratory of Advanced Combinatorics and Network Applications, 9 Institutskiy per., Dolgoprodny, Moscow Region 141701, Russian Federation

2. Adyghe State University, Caucasus Mathematical Center, ul. Pervomayskaya, 208, Maykop, Republic of Adygea, 385000, Russian Federation

3. The Russian Presidential Academy of National Economy and Public Administration, Prospect Vernadskogo, 84, bldg 2, Moscow 119571, Russian Federation

Abstract

In 2001, Le Bars proved that there exists an existential monadic second-order (EMSO) sentence such that the probability that it is true on [Formula: see text] does not converge and conjectured that, for EMSO sentences with two first-order variables, the zero–one law holds. In this paper, we prove that the conjecture fails for [Formula: see text], and give new examples of sentences with fewer variables without convergence (even for [Formula: see text]).

Funder

Russian Science Foundation

Publisher

World Scientific Pub Co Pte Lt

Subject

Logic

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219061320500075

Reference19 articles.

1. The Probabilistic Method

2. Random Graphs

3. A logical approach to asymptotic combinatorics II: Monadic second-order properties

4. Finite Model Theory

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