It is proved that the 0-1 law does not hold for the class of existential second sentences whose first order part is in the minimal Godel class, i.e. has the quantifier prenex consisting of two universal quantifiers followed by just one existential quantifier. This completes the classification of existential second order sentences for which the 0-1 law holds. It is also proved that asymptotic probabilities of sentences as above form a dense subset of the unit interval.
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