# Sh:953

• Doron, M., & Shelah, S. (2010). Hereditary zero-one laws for graphs. In Fields of logic and computation, Vol. 6300, Springer, Berlin, pp. 581–614.
• 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 probabilitie. 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.
• Current version: 2010-04-04_11 (30p) published version (34p)
Bib entry
@incollection{Sh:953,
author = {Doron, Mor and Shelah, Saharon},
title = {{Hereditary zero-one laws for graphs}},
booktitle = {{Fields of logic and computation}},
series = {Lecture Notes in Comput. Sci.},
volume = {6300},
year = {2010},
pages = {581--614},
publisher = {Springer, Berlin},
mrnumber = {2756404},
mrclass = {03C13},
doi = {10.1007/978-3-642-15025-8_29},
note = {\href{https://arxiv.org/abs/1006.2888}{arXiv: 1006.2888}},
arxiv_number = {1006.2888}
}