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  1. Completeness in the Theory of Types.Leon Henkin - 1950 - Journal of Symbolic Logic 15 (2):81-91.
  • A Formulation of the Simple Theory of Types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (2):56-68.
  • A Partial Functions Version of Church's Simple Theory of Types.William M. Farmer - 1990 - Journal of Symbolic Logic 55 (3):1269-1291.
    Church's simple theory of types is a system of higher-order logic in which functions are assumed to be total. We present in this paper a version of Church's system called PF in which functions may be partial. The semantics of PF, which is based on Henkin's general-models semantics, allows terms to be nondenoting but requires formulas to always denote a standard truth value. We prove that PF is complete with respect to its semantics. The reasoning mechanism in PF for partial (...)
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  • A Theory of Propositional Types.Leon Henkin - 1963 - Fundamenta Mathematicae 52:323-334.
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  • A Reduction of the Axioms for the Theory of Propositional Types.Peter Andrews - 1963 - Fundamenta Mathematicae 52:345-350.
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