Abstract
AbstractWe propose an original use of techniques from random graph theory to find a Monadic(Minimal Scott without equality) sentence without an asymptotic probability. Our result implies that the 0-1 law fails for the logics(FO2) and](Minimal Gödel without equality). Therefore we complete the classification of first-order prefix classes with or without equality, according to the existence of the 0-1 law for the correspondingfragment. In addition, our counterexample can be viewed as a single explanation of the failure of the 0-1 law of all the fragments of existential second-order logic for which the failure is already known.
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