Geodesic
Zero-one laws for graphs with edge probabilities decaying with distance. Part I
Saharon Shelah1
1 Institute of Mathematics The Hebrew University of Jerusalem 91904 Jerusalem, Israel
Fundamenta Mathematicae, Tome 175 (2002) no. 3, pp. 195-239.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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..
DOI : 10.4064/fm175-3-1
Keywords: random graph ldots possible edge having probability i j i j alpha i alpha irrational prove zero one law first order logic holds

Saharon Shelah 1

1 Institute of Mathematics The Hebrew University of Jerusalem 91904 Jerusalem, Israel 
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Saharon Shelah. Zero-one laws for graphs with edge
 probabilities decaying with distance. Part I. Fundamenta Mathematicae, Tome 175 (2002) no. 3, pp. 195-239. doi : 10.4064/fm175-3-1. http://geodesic.mathdoc.fr/articles/10.4064/fm175-3-1/

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