Nonconstructive Computational Mathematics

Authors:
Kenneth Kunen
Affiliations:
University of Wisconsin, Madison, WI 53706, U.S.A. e-mail:kunen@math.wisc.edu
Venue:
Journal of Automated Reasoning
Year:
1998

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Abstract

We describe a nonconstructive extension to primitive recursivearithmetic, both abstractly and as implemented on the Boyer-Moore prover.Abstractly, this extension is obtained by adding the unbounded µoperator applied to primitive recursive functions; doing so, one can definethe Ackermann function and prove the consistency of primitive recursivearithmetic. The implementation does not mention the µ operatorexplicitly but has the strength to define the µ operator through thebuilt-in functions EVAL$ and V&C$.