Hereditary Zero-One Laws for Graphs
Logic
2010-06-16 v1 Combinatorics
Abstract
We consider the random graph M^n_{\bar{p}} on the set [n], were the probability of {x,y} being an edge is p_{|x-y|}, and \bar{p}=(p_1,p_2,p_3,...) is a series of probabilities. We consider the set of all \bar{q} derived from \bar{p} by inserting 0 probabilities to \bar{p}, or alternatively by decreasing some of the p_i. We say that \bar{p} hereditarily satisfies the 0-1 law if the 0-1 law (for first order logic) holds in M^n_{\bar{q}} for any \bar{q} derived from \bar{p} in the relevant way described above. We give a necessary and sufficient condition on \bar{p} for it to hereditarily satisfy the 0-1 law.
Keywords
Cite
@article{arxiv.1006.2888,
title = {Hereditary Zero-One Laws for Graphs},
author = {Mor Doron and Saharon Shelah},
journal= {arXiv preprint arXiv:1006.2888},
year = {2010}
}