Higher-Order Illative Combinatory Logic

  title={Higher-Order Illative Combinatory Logic},
  author={Lukasz Czajka},
  journal={The Journal of Symbolic Logic},
  pages={837 - 872}
  • Lukasz Czajka
  • Published 16 February 2012
  • Mathematics
  • The Journal of Symbolic Logic
Abstract We show a model construction for a system of higher-order illative combinatory logic thus establishing its strong consistency. We also use a variant of this construction to provide a complete embedding of first-order intuitionistic predicate logic with second-order propositional quantifiers into the system of Barendregt, Bunder and Dekkers, which gives a partial answer to a question posed by these authors. 

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