9 citations · 24 across the 7 of their papers we have counts for
9 papers
Naïve Infinitesimal Analysis: Its Construction and Its Properties
Anggha Nugraha, Maarten McKubre-Jordens, Hannes Diener
This paper aims to build a new understanding of the nonstandard mathematical analysis. The main contribution of this paper is the construction of a new set of numbers, $\mathbb{R}^…
(Seemingly) Impossible Theorems in Constructive Mathematics
Hannes Diener, Matthew Hendtlass
We prove some constructive results that on first and maybe even on second glance seem impossible.
The Drinker Paradox and its Dual
Louis Warren, Hannes Diener, Maarten McKubre-Jordens
The Drinker Paradox is as follows. In every nonempty tavern, there is a person such that if that person is drinking, then everyone in the tavern is drinking. Formally, \[ \exists x…
Constructive Reverse Mathematics
Hannes Diener
An introduction and overview of constructive reverse mathematics.
The Third Trick
Hannes Diener, Matthew Hendtlass
We prove a result, similar to the ones known as Ishihara's First and Second Trick, for sequences of functions.
Classifying Material Implications over Minimal Logic
Hannes Diener, Maarten McKubre-Jordens
The so-called paradoxes of material implication have motivated the development of many non-classical logics over the years \cite{aA75,nB77,aA89,gP89,sH96}. In this note, we investi…
Separating the Fan Theorem and Its Weakenings
Robert S. Lubarsky, Hannes Diener
Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational h…
Principles Weaker than BD-N
Robert S. Lubarsky, Hannes Diener
BD-N is a weak principle of constructive analysis. Several interesting principles implied by BD-N have already been identified, namely the closure of the anti-Specker spaces under…
Constructive aspects of Riemann's permutation theorem for series
J. Berger, D. Bridges, H. Diener +1
The notions of permutable and weak-permutable convergence of a series of real numbers are introduced. Classically, these two notions are equivalent, and,…