On failure of 0-1 laws

by Shelah. [Sh:1061]
Fields Logic and Computation II (Yurifest Workshop), 2015
Let alpha in (0,1)_{{R}} be irrational and G_n = G_{n,1/n^alpha} be the random graph with edge probability 1/n^alpha ; we know that it satisfies the 0-1 law for first order logic. We deal with the failure of the 0-1 law for stronger logics: {L}_{infty,k},k large enough and the inductive logic.

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