Zero-one laws for graphs with edge probabilities decaying with distance. Part I
Volume 175 / 2002
Fundamenta Mathematicae 175 (2002), 195-239
MSC: 03C13, 60F20, 03C10.
DOI: 10.4064/fm175-3-1
Abstract
Let $G_n$ be the random graph on $[n]=\{1,\ldots,n\}$ with the possible edge $\{i,j\}$ having probability $p_{|i-j|}= 1/|i-j|^\alpha$ for $j\ne i, i+1, i-1$ with $\alpha\in (0,1)$ irrational. We prove that the zero-one law (for first order logic) holds..
