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

Saharon Shelah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

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 aψn be the probability of Mn |= ψ. We know that the sequence aψ1, aψ2, . . . , aψn, . . . does not necessarily converge. But here we find a weaker substitute which we call the very weak 0-1 law. We prove that limn → ∞(aψn - aψn+1) = 0. For this we need a theorem on the (first-order) theory of distorted sum of models.

Original languageEnglish
Pages (from-to)137-159
Number of pages23
JournalJournal of Logic and Computation
Volume6
Issue number1
DOIs
StatePublished - Feb 1996

Keywords

  • Random graphs
  • Sum of models
  • Zero one law

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