This paper extends the admissibility condition of the Modal-Dependence Calculus (MDC) from finite sequences to indexed families of transformations. An indexed family is admissible if and only if every indexed element satisfies the condition tau(x) = 1, corresponding to the definability of the dependence relation D*(x, c). Admissibility is therefore governed by a universal condition over the entire indexed domain rather than a finite, stepwise conjunction. The existence of any indexed element for which tau(x) = 0 is sufficient to yield non-admissibility. This establishes that admissibility across arbitrary domains is determined by the universal preservation of definability relative to the invariant core.
Austin Jacobs (Sun,) studied this question.