Strong failure of 0-1 law for LFP and the path logics

by Shelah. [Sh:1096]

we continue [1062], in two issues. First we introduce a logic, called path logic which seem natural

there and try to prove for it the 0-1 law Second, for the random graph G_{n, n^alpha} in [1062] we get only a weak failure of the 01 law, the truth value of the sentence

is sometimes close to 1 and sometimes close to 0, but it change slowly. Here we intend to prove that tehere is an interpretaion which for a random enough graph give number theory on n, so we can ``define n being odd/even''

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