Failure of 0-1 law for sparse random graph in strong logics
Saharon Shelah · arXiv (Cornell University) · 2017
Let $α\in(0,1)_\mathbb{R}$ be irrational and $G_n = G_{{n, 1/n}^α}$ be the random graph with edge probability $1/n^α$; 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 LFP, least fix point logic.