Year: 2016
Type: preprint
Abstract: In this paper the limit probabilities of first-order properties are studied. The random graph $G(n,p)$ {\it obeys Zero-One $k$-Law} if for each first-order property with quantifier depth not greater than $k$ its probability tends to 0 or tends to 1. We found an explicit interval to the left of any rational point on which the Zero-One $k$-Law holds. We also proved, that if $t/s$ is a rational number with numerator not greater than 2, then logarithm of our interval's length has the same asymptotics up to a constant factor (when $n\rightarrow\infty$) as logarithm of the biggest interval with right end at $(t/s)$ on which Zero-One $k$-Law holds.
Source: arXiv (Cornell University)
Author: Matushkin, Aleksandr
Institution: Moscow Institute of Physics and Technology
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2260338304