A constructive approach to nonstandard analysis

A Constructive Approach to Nonstandard Analysis

In the present paper we introduce a constructive theory of nonstandard arithmetic in higher types. The theory is intended as a framework for developing elementary nonstandard analysis constructively. More specifically, the theory introduced is a conservative extension of HA” + AC. A predicate for distinguishing standard objects is added as in Nelson’s internal set theory. Weak transfer and idea...

A New Approach to Nonstandard Analysis

In this paper, we propose a new approach to nonstandard analysis without using the ultrafilters. This method is very simple in practice. Moreover, we construct explicitly the total order relation in the new field of the infinitesimal numbers. To illustrate the importance of this work, we suggest comparing  a few applications of this approach with the former methods.

Unifying Constructive and Nonstandard Analysis

Remarks on a Constructive Sheaf Model of Nonstandard Analysis

The sheaves over the category of lters, with a joint cover topology, serve as a universe of sets where nonstandard analysis can be developed along constructive principles. In this paper we show that all functions between internal sets in this model are internal. We also illustrate how this model can be used by giving a constructive nonstandard proof of the Implicit Function Theorem.

Translating nonstandard proofs to constructive ones

From 09.01.05 to 14.01.05, the Dagstuhl Seminar 05021 Mathematics, Algorithms, Proofs was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results an...