Journal of Symbolic Logic 62 (1):304-319 (1997)
We show that the 0-1 law does not hold for the class Σ 1 1 (∀∃∀ without =) by finding a sentence in this class which almost surely expresses parity. We also show that every recursive real in the unit interval is the asymptotic probability of a sentence in this class. This expands a result by Lidia Tendera, who in 1994 proved that every rational number in the unit interval is the asymptotic probability of a sentence in the class Σ 1 1 ∀∃∀ with equality
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Counterexamples of the 0-1 Law for Fragments of Existential Second-Order Logic: An Overview.Le Bars Jean-Marie - 2000 - Bulletin of Symbolic Logic 6 (1):67-82.
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