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First order properties of random posets

✍ Scribed by Tomasz Łuczak

Publisher
Springer Netherlands
Year
1991
Tongue
English
Weight
397 KB
Volume
8
Category
Article
ISSN
0167-8094

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✦ Synopsis

Let LB = s2(n, p) be a binary relation on the set [n] = { 1, ?, , n} such that Se(i, i) for every i and W(i,j) with probability p, independently for each pair i, j E [n], where i <j. Define < as the transitive closure of W and denote poset ([n], <) by R(n, p). We show that for any constant p probability of each first order property of R(n, p) converges as n + co.

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