System T, System F and Arithmetic Hierarchy

I refer to Proof and Types by Jean-Yves Girard for the definition of System T (page 46) and System F (page 81).
There are two basic types in this paper, d. H. e. $ text {Int} $ (natural numbers) and $ text {Bool} $ (booleans), so I assume that the guy $ text {Int} rightarrow text {Bool} $ can be seen as Set of natural numbers, This gives me a curiosity: what is the position of the sets of system T in the arithmetic hierarchy? and about the sets of system F?
I searched the literature but did not find anything.