Note on extensions of Heyting's arithmetic by adding the ``creative subject''
It is shown that the extension of Heyting's arithmetic HA by Kreisel's axioms for the creative subject [see \textit{A. S. Troelstra} and \textit{D. van Dalen}, Constructivism in mathematics. Vol. 1 (North-Holland, Amsterdam) (1988; Zbl 0653.03040), p. 236], with the induction schema restricted to arithmetical formulae, is conservative over HA. Some interesting generalizations of this result are considered in the last part of the paper. The proofs are based on the model-theoretic method.
scientific article; zbMATH DE number 1348069