# 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. arXiv: 1006.2888 DOI: 10.1007/978-3-642-15025-8_29 MR: 2756404 -
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. - 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}, doi = {10.1007/978-3-642-15025-8_29}, mrclass = {03C13}, mrnumber = {2756404}, doi = {10.1007/978-3-642-15025-8_29}, publisher = {Springer, Berlin}, note = {\href{https://arxiv.org/abs/1006.2888}{arXiv: 1006.2888}}, arxiv_number = {1006.2888} }