Zero-one laws for graphs with edge probabilities decaying with distance. Part I
Saharon Shelah · Fundamenta Mathematicae · 2002
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 $j e i, i+1, i-1$ with $\alpha\in (0,1)$ irrational. We prove that the zero-one law (for first order logic) holds..