6 papers · 1 filter
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 the computational properties of basic mathematical notions
Dag Normann, Sam Sanders
We investigate the computational properties of basic mathematical notions pertaining to -functions and subsets of , like finiteness, c…
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…
On sequential theorems in Reverse Mathematics
Dag Normann, Sam Sanders
Many theorems of mathematics have the form that for a certain problem, e.g. a differential equation or polynomial (in)equality, there exists a solution. The sequential version then…