What evidence is there that 2ˆ65536 is a natural number?

Abstract

The closure of the natural numbers under exponentiation a'ˆb is a fact which is central to results in metamathematics. The argument which purports to establish this closure involves a simple mathematical induction. An analysis of this proof shows that it may involve a new and subtle form of circularity. © 1992 by the University of Notre Dame. All rights reserved.