×

On the theory of models for intuitionistic logic. (English. Russian original) Zbl 0568.03018

Math. USSR, Sb. 48, 223-235 (1984); translation from Mat. Sb., Nov. Ser. 120(162), No. 2, 227-239 (1983).
A model approach is developed for intuitionistic and classical theories in the language of the simple theory of types. A weak form of completeness theorem is proved, of which the Henkin completeness theorem is a special case. An ultraproduct of Kripke structures is introduced, and an application of the omitting types theorem to theories with infinite rules for deduction is given.

MSC:

03C95 Abstract model theory
03F55 Intuitionistic mathematics
03C20 Ultraproducts and related constructions
03C35 Categoricity and completeness of theories
03B15 Higher-order logic; type theory (MSC2010)
03B55 Intermediate logics
PDF BibTeX XML Cite
Full Text: DOI