A Nonstandard Counterpart of WWKL

Comparing DNR and WWKL

In Reverse Mathematics, the axiom system DNR, asserting the existence of diagonally non-recursive functions, is strictly weaker than WWKL0 (weak weak König’s

Vitali's Theorem and WWKL

Continuing the investigations of X. Yu and others, we study the role of set existence axioms in classical Lebesgue measure theory. We show that pairwise disjoint countable additivity for open sets of reals is provable in RCA0. We show that several well-known measure-theoretic propositions including the Vitali Covering Theorem are equivalent to WWKL over RCA0.

FOUNDATIONS OF NONSTANDARD ANALYSIS A Gentle Introduction to Nonstandard Extensions

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.

A Combination of Nonstandard Analysis

The theorem prover Isabelle is used to formalise and reproduce some of the styles of reasoning used by Newton in his Principia. The Principia's reasoning is resolutely geometric in nature but contains \in nitesimal" elements and the presence of motion that take it beyond the traditional boundaries of Euclidean Geometry. These present di culties that prevent Newton's proofs from being mechanised...