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On the very weak 0 − 1 law for random graphs with orders

By Saharon Shelah


Abstract: Let us draw a graph R on {0, 1,..., n − 1} by having an edge {i, j} with probability p |i−j|, where ∑ i pi < ∞, and let Mn = (n, <, R). For a first order sentence ψ let an ψ be the probability of Mn | = ψ. We know that the sequence a1 ψ, a2 ψ,..., an ψ,... does not necessarily converge. But here we find a weaker substitute which we call the very weak 0-1 law. We prove that limn→∞(an ψ − an+1 ψ) = 0. For this we need a theorem on the (first order) theory of distorted sum of models

Year: 1996
DOI identifier: 10.1093/logcom/6.1.137
OAI identifier: oai:CiteSeerX.psu:
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