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  1. Decidability Problems in Languages with Henkin Quantifiers.Michał Krynicki & Marcin Mostowski - 1992 - Annals of Pure and Applied Logic 58 (2):149-172.
    Krynicki, M. and M. Mostowski, Decidability problems in languages with Henkin quantifiers, Annals of Pure and Applied Logic 58 149–172.We consider the language L with all Henkin quantifiers Hn defined as follows: Hnx1…xny1…yn φ iff f1…fnx1. ..xn φ, ...,fn). We show that the theory of equality in L is undecidable. The proof of this result goes by interpretation of the word problem for semigroups.Henkin quantifiers are strictly related to the function quantifiers Fn defined as follows: Fnx1…xny1…yn φ iff fx1…xn φ,...,f). (...)
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  • Degrees of Logics with Henkin Quantifiers in Poor Vocabularies.Marcin Mostowski & Konrad Zdanowski - 2004 - Archive for Mathematical Logic 43 (5):691-702.
    We investigate some logics with Henkin quantifiers. For a given logic L, we consider questions of the form: what is the degree of the set of L–tautologies in a poor vocabulary (monadic or empty)? We prove that the set of tautologies of the logic with all Henkin quantifiers in empty vocabulary L*∅ is of degree 0’. We show that the same holds also for some weaker logics like L ∅(Hω) and L ∅(Eω). We show that each logic of the form (...)
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