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We study different representation theorems for various reducts of Heytingpolyadic algebras. Superamalgamation is proved for several (natural reducts)and our results are compared to the finitizability problem in classicalalgebraic logic dealing with cylindric and polyadic (Boolean algebras). We alsoprove several new neat embedding theorems, and obtain that the class ofrepresentable algebras based on (a generalized) Kripke semantics coincide withthe class of algebras having the neat embedding property, that is thosealgebras that are subneat reducts of algebras having $\omega$ extra dimensions.

Completeness and interpolation for intuitionistic infinitary predicate  logic, in connection to finitizing the class of representable Heyting  polyadic algebras