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arXiv · 1706.01226

Failure of 0-1 law for sparse random graph in strong logics

Saharon Shelah
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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 LFP, least fix point logic.

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Saharon Shelah. 2017-06-05. Failure of 0-1 law for sparse random graph in strong logics. https://arxiv.org/abs/1706.01226

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