## Journal of Symbolic Logic

### Higher-order illative combinatory logic

łukasz Czajka

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 6 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1389032278

Digital Object Identifier
doi:10.2178/jsl.7803080

Mathematical Reviews number (MathSciNet)
MR3135501

Zentralblatt MATH identifier
1341.03018

#### Citation

Czajka, łukasz. Higher-order illative combinatory logic. J. Symbolic Logic 78 (2013), no. 3, 837--872. doi:10.2178/jsl.7803080. https://projecteuclid.org/euclid.jsl/1389032278