Explicit Mathematics With The Monotone Fixed Point Principle. II: Models

This paper continues investigations of the monotone fixed point principle in the context of Feferman's explicit mathematics begun in [14]. Explicit mathematics is a versatile formal framework for representing Bishop-style constructive mathematics and generalized recursion theory. The object of investigation here is the theory of explicit mathematics augmented by the monotone fixed point principle, which asserts that any monotone operation on classifications (Feferman's notion of set) possesses a least fixed point. To be more precise, the new axiom not merely postulates the existence of a least solution, but, by adjoining a new constant to the language, it is ensured that a fixed point is uniformly presentable as a function of the monotone operation. Let T 0 +UMID denote this extension of explicit mathematics. [14] gave lower bounds for the strength of two subtheories of T 0 +UMID in relating them to fragments of second order arithmetic based on \Pi 1 2 comprehension. [14] showed that ..