Zero-one laws for k-variable first-order logic of sparse random graphs [article]

A.S. Razafimahatratra, M. Zhukovskii
2019 arXiv   pre-print
In this paper, we prove that for every positive ε, there exists an α∈(1/(k-1),1/(k-1)+ε) such that the binomial random graph G(n,n^-α) does not obey 0-1 law w.r.t. first order sentences with k variables. In contrast, for every α∈(0,1/(k-1)], G(n,n^-α) obeys 0-1 law w.r.t. this logic.
arXiv:1811.07026v2 fatcat:2sa3ztzqgra6xmoquaefr4f63i