Hereditary Zero-One Laws for Graphs
نویسندگان
چکیده
We consider the random graph M n ¯ p on the set [n], were the probability of {x, y} being an edge is p |x−y| , and ¯ p = (p 1 , p 2 , p 3 , ...) is a series of probabilities. We consider the set of all ¯ q derived from ¯ p by inserting 0 probabilities to ¯ p, or alternatively by decreasing some of the p i. We say that ¯ p hereditarily satisfies the 0-1 law if the 0-1 law (for first order logic) holds in M n ¯ q for any ¯ q derived from ¯ p in the relevant way described above. We give a necessary and sufficient condition on ¯ p for it to hereditarily satisfy the 0-1 law.
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