Weak theories of nonstandard arithmetic and analysis

Abstract

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.

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Jeremy Avigad
Carnegie Mellon University

Citations of this work

Erna and Friedman's reverse mathematics.Sam Sanders - 2011 - Journal of Symbolic Logic 76 (2):637 - 664.
Number theory and elementary arithmetic.Jeremy Avigad - 2003 - Philosophia Mathematica 11 (3):257-284.
A functional interpretation for nonstandard arithmetic.Benno van den Berg, Eyvind Briseid & Pavol Safarik - 2012 - Annals of Pure and Applied Logic 163 (12):1962-1994.
Forcing in proof theory.Jeremy Avigad - 2004 - Bulletin of Symbolic Logic 10 (3):305-333.
On the strength of nonstandard analysis.C. Ward Henson & H. Jerome Keisler - 1986 - Journal of Symbolic Logic 51 (2):377-386.

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References found in this work

Handbook of proof theory.Samuel R. Buss (ed.) - 1998 - New York: Elsevier.
Interpreting classical theories in constructive ones.Jeremy Avigad - 2000 - Journal of Symbolic Logic 65 (4):1785-1812.
A feasible theory for analysis.Fernando Ferreira - 1994 - Journal of Symbolic Logic 59 (3):1001-1011.

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