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This work contains the formula part of the presentation of the mathematical logic R0, a further development of Peter B. Andrews' logic Q0. The syntactic features provided by R0 are type variables (polymorphic type theory), the binding of type variables with the abstraction operator and single variable binder (type abstraction), and (some of) the means necessary for dependent types (dependent type theory).For more information, please visit: http://doi.org/10.4444/100.10