Date of Original Version
Reverse mathematics 2001. Edited by Stephen G. Simpson. Wellesley, Mass.: A K Peters, Ltd., 2005: 19-46.
Abstract or Table of Contents
A general method of interpreting weak higher-type theories of nonstandard arithmetic in their standard counterparts is presented. In particular, this provides natural nonstandard conservative extensions of primitive recursive arithmetic, elementary recursive arithmetic, and polynomial-time computable arithmetic. A means of formalizing basic real analysis in such theories is sketched.