Third-Order Computation and Bounded Arithmetic
Alan Ramsay Skelley · Journal of Logic and Computation · 2007
Abstract. We describe a natural generalization of ordinary computation to a third-order setting and give a function calculus with nice properties and recursion-theoretic characterizations of several large complexity classes. We then present a number of third-order theories of bounded arithmetic whose definable functions are the classes of the EXP-time hierarchy in the third-order setting.