On failure of 0-1 laws

Saharon Shelah

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arXiv · 2108.03846

On failure of 0-1 laws

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 inductive logic.

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Saharon Shelah. 2021-08-09. On failure of 0-1 laws. https://arxiv.org/abs/2108.03846

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