Embedding intuitionistic-type theory in negationless-type theory
In ''A formal system of negationless arithmetic that is consistent with respect to Heyting arithmetic'' [Mat. Zametki 36, No.4, 583-592 (1984; Zbl 0576.03037)] the author shows that Heyting arithmetic is a conservative extension of \(HA^ N\)- a system of negationless arithmetic, under certain interpretation. Here he extends this result to the case of intuitionistic type theory HATT and a system of negationless type theory HATTN.
scientific article; zbMATH DE number 3993583