Heyting valued set theory and Sato hyperfunctions (Q1820158)

\textit{C. Rousseau} [Lect. Notes Math. 753, 623-659 (1979; Zbl 0433.32003)] has demonstrated that standard function theory of n variables is no other than intuitionistic function theory of one variable over \(C^{n-1}\). \textit{G. Takeuti} and \textit{S. Titani} [Global intuitionistic analysis, Preprint] have pursued the same idea in the realm of complex manifolds to find out that vector bundles over a complex manifold are apartness vector spaces, that families of complex structures are simply complex manifolds, and so on. Following these lines, this paper shows that Sato hyperfunctions with holomorphic parameters can be viewed as those without parameters in an appropriately chosen intuitionistic universe, where we establish, as an application of this idea, de Rham and Dolbeault theorems with hyperfunctional coefficients.