## Weak theories of nonstandard arithmetic and analysis (2001)

Venue: | Reverse Mathematics |

Citations: | 7 - 5 self |

### BibTeX

@INPROCEEDINGS{Avigad01weaktheories,

author = {Jeremy Avigad},

title = {Weak theories of nonstandard arithmetic and analysis},

booktitle = {Reverse Mathematics},

year = {2001}

}

### OpenURL

### Abstract

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. §1. Introduction. Nonstandard analysis, as developed by Abraham Robinson, provides an elegant paradigm for the application of metamathematical ideas in mathematics. The idea is simple: use model-theoretic methods to build rich extensions of a mathematical structure, like second-order arithmetic or a universe of sets; reason about what is true in these enriched structures;