A Note On Asymptotic Probabilities Of Existential Second-Order Minimal Classes - The Last Step

Authors:
Lidia Tendera
Affiliations:
Institute of Mathematics, Pedagogical University, Oleska 48, 45-951 Opole, Poland
Venue:
Fundamenta Informaticae
Year:
1994

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Abstract

The Σ11(∀∃∀) class is the class of all existential second-order sentences whose first-order part is in the prenex form with prefix of the form ∀∃∀. In this paper we prove that every rational number in the interval [0,1] is the asymptotic probability for some Σ11(∀∃∀) sentence. This result completes the classification of asymptotic probabilities for the existential second-order minimal classes.