Relative Constructivity

In a previous paper [10] we introduced a hierarchy (GnA )n∈IN of subsystems of classical arithmetic in all finite types where the growth of definable functions of GnA ω corresponds to the well–known Grzegorczyk hierarchy. Let AC–qf denote the schema of quantifier–free choice. [8],[10] and subsequent papers (under preparation) study various analytical principles Γ in the context of the theories GnA +AC–qf (mainly for n = 2) and use proof–theoretic tools like e.g. monotone functional interpretation (which was introduced in [9]) to determine their impact on the growth of uniform bounds Φ such that