On the very weak 0-1 law for random graphs with orders
Abstract
Let us draw a graph R on 0,1,...,n-1 by having an edge i,j with probability p(|i-j|), where sumi pi is finite and let Mn=(n,<,R). For a first order sentence psi let anpsi be the probability of ``Mn satisfies psi''. We prove that the limit of anpsi-an+1psi is 0, as n goes to infinity.
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