A NOTE ON ASYMPTOTIC PROBABILITIES OF EXISTENTIAL SECOND-ORDER MINIMAL CLASSES – THE LAST STEP

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.