Abstract
We describe a natural generalization of ordinary computation to a third-order (i.e. three-sorted) setting. We give a function calculus with nice properties and recursion-theoretic characterizations of several large complexity classes, including classes of functions and predicates from the levels of the exponential-time hierarchy. We then present a number of third-order theories of bounded arithmetic whose definable functions are the classes of the exponential time hierarchy in the third-order setting.
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