A counterexample to the 0-1 law for the class of existential second-order minimal Gödel sentences with equality
It is shown that the 0-1 law fails for the class of existential second- order sentences whose first-order part is of the form \(\forall x\forall y\exists z\varphi(x,y,z)\) with quantifier-free \(\varphi\). This result completes the characterization of the classes of existential second-order sentences according to its first-order quantifier prefix, for which the 0-1 law holds. It coincides with the characterization of the solvable cases of the decision problem.
scientific article; zbMATH DE number 529887