TY - JOUR
T1 - On the very weak 0-1 law for random graphs with orders
AU - Shelah, Saharon
PY - 1996/2
Y1 - 1996/2
N2 - Let us draw a graph R on {0, 1, . . . , n - 1} by having an edge {i, j} with probability p\i-j\, where ∑i pi < ∞, and let Mn = (n, <, R). For a first-order sentence ψ let aψn be the probability of Mn |= ψ. We know that the sequence aψ1, aψ2, . . . , aψn, . . . does not necessarily converge. But here we find a weaker substitute which we call the very weak 0-1 law. We prove that limn → ∞(aψn - aψn+1) = 0. For this we need a theorem on the (first-order) theory of distorted sum of models.
AB - Let us draw a graph R on {0, 1, . . . , n - 1} by having an edge {i, j} with probability p\i-j\, where ∑i pi < ∞, and let Mn = (n, <, R). For a first-order sentence ψ let aψn be the probability of Mn |= ψ. We know that the sequence aψ1, aψ2, . . . , aψn, . . . does not necessarily converge. But here we find a weaker substitute which we call the very weak 0-1 law. We prove that limn → ∞(aψn - aψn+1) = 0. For this we need a theorem on the (first-order) theory of distorted sum of models.
KW - Random graphs
KW - Sum of models
KW - Zero one law
UR - http://www.scopus.com/inward/record.url?scp=0002358809&partnerID=8YFLogxK
U2 - 10.1093/logcom/6.1.137
DO - 10.1093/logcom/6.1.137
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AN - SCOPUS:0002358809
SN - 0955-792X
VL - 6
SP - 137
EP - 159
JO - Journal of Logic and Computation
JF - Journal of Logic and Computation
IS - 1
ER -