5 papers
The uncountability of the reals and the Axiom of Choice
Dag Normann, Sam Sanders
The uncountability of the reals was first established by Cantor in what was later heralded as the first paper on set theory. Since the latter constitutes the official foundations o…
On the computational properties of ambivalent sets and functions
Dag Normann, Sam Sanders
Examples of discontinuous functions already appear in the work of Euler, Abel, Dirichlet, Fourier, and Bolzano. A ground-breaking discovery due to Baire was that many discontinuous…
On some computational properties of open sets
Dag Normann, Sam Sanders
Open sets are central to mathematics, especially analysis and topology, in ways few notions are. In most, if not all, computational approaches to mathematics, open sets are only st…
On two recent extensions of the Big Five of Reverse Mathematics
Dag Normann, Sam Sanders
The program Reverse Mathematics in the foundations of mathematics seeks to identify the minimal axioms required to prove theorems of ordinary mathematics. One always assumes the ba…
Approximation theorems throughout Reverse Mathematics
Sam Sanders
Reverse Mathematics (RM for short) is a program in the foundations of mathematics where the aim is to find the minimal axioms needed to prove a given theorem of ordinary mathematic…