Journal of Symbolic Logic

Higher-order illative combinatory logic

łukasz Czajka

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We show a model construction for a system of higher-order illative combinatory logic $\mathcal{I}_\omega$, 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 $\mathcal{I}_0$ of Barendregt, Bunder and Dekkers, which gives a partial answer to a question posed by these authors.

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J. Symbolic Logic, Volume 78, Issue 3 (2013), 837-872.

First available in Project Euclid: 6 January 2014

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Czajka, łukasz. Higher-order illative combinatory logic. J. Symbolic Logic 78 (2013), no. 3, 837--872. doi:10.2178/jsl.7803080.

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