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

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

1996-06-15

arxiv.org/abs/math/9606226v2

Fundamenta Mathematicae 175(2002):195-239

Mathematics

Logic

Scientific paper

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]

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