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  1. Counterexamples of the 0-1 Law for Fragments of Existential Second-Order Logic: An Overview.Jean-Marie le Bars - 2000 - Bulletin of Symbolic Logic 6 (1):67-82.
    We propose an original use of techniques from random graph theory to find a Monadic ∑ 1 1 sentence without an asymptotic probability. Our result implies that the 0-1 law fails for the logics ∑ 1 1 and ∑ 1 1 . 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 corresponding ∑ 1 1 fragment. In addition, our counterexample can be viewed as a single explanation (...)
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