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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2005 | 185 | 3 | 211-245

## Zero-one laws for graphs with edge probabilities decaying with distance. Part II

EN

### Abstrakty

EN
Let Gₙ be the random graph on [n] = {1,...,n} with the probability of {i,j} being an edge decaying as a power of the distance, specifically the probability being $p_{|i-j|} = 1/|i-j|^{α}$, where the constant α ∈ (0,1) is irrational. We analyze this theory using an appropriate weight function on a pair (A,B) of graphs and using an equivalence relation on B∖A. We then investigate the model theory of this theory, including a "finite compactness". Lastly, as a consequence, we prove that the zero-one law (for first order logic) holds.

211-245

wydano
2005

### Twórcy

autor
• Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 91904, Israel
• Department of Mathematics, Rutgers, The State University of New Jersey, Hill Center-Busch Campus, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, U.S.A.