On failure of 0-1 laws

Abstract

Let $\alpha \in (0,1{)}_{\mathbb{R}}$ be irrational and $G_n=G_{n,1/n^{\alpha }}$ be the random graph with edge probability $1/n^{\alpha }$; we know that it satisfies the 0-1 law for first order logic. We deal with the failure of the 0-1 law for stronger logics: ${\mathbb{L}}_{\infty ,k},k$ large enough and the inductive logic.

arXiv admin note: substantial text overlap with arXiv:1706.01226