Following the lines of Takeuti and Titani  as well as Rousseau , 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.
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Hirokazu Nishimura, Heyting Valued Set Theory and Sato Hyperfunctions. Publ. Res. Inst. Math. Sci. 22 (1986), no. 4, pp. 801–811DOI 10.2977/PRIMS/1195177631