English

Zero one laws for graphs with edge probabilities decaying with distance. Part I

Logic 2009-09-25 v2 Combinatorics

Abstract

Let G_n be the random graph on [n]= {1, ...,n} with the possible edge {i,j} having probability being p_{|i-j|}= 1/|i-j|^alpha, alpha in (0,1) irrational. We prove that the zero one law (for first order logic) holds. The paper is continued in [Sh:517]

Keywords

Cite

@article{arxiv.math/9606226,
  title  = {Zero one laws for graphs with edge probabilities decaying with distance. Part I},
  author = {Saharon Shelah},
  journal= {arXiv preprint arXiv:math/9606226},
  year   = {2009}
}
R2 v1 2026-07-22T17:56:17.513Z