✦ LIBER ✦

Very weak zero one law for random graphs with order and random binary functions

✍ Scribed by Saharon Shelah

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 450 KB
Volume: 9
Category: Article
ISSN: 1042-9832
DOI: 10.1002/(sici)1098-2418(199612)9:4<351::aid-rsa1>3.0.co;2-w

No coin nor oath required. For personal study only.

✦ Synopsis

Natural languages and random structures are given for which there are sentences A with no limit probability, yet for every A the difference between the probabilities that A holds on random structures of sizes n and n + 1 approaches zero with n.

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We look at a competitor of the Erdos᎐Renyi models of random graphs, one ˝ẃ Ž .x proposed in E. Gilbert J. Soc. Indust. Appl. Math. 9:4, 533᎐543 1961 : given ␦ ) 0 and a metric space X of diameter ) ␦ , scatter n vertices at random on X and connect those of distance -␦ apart: we get a random graph G