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math.LO2024
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…
math.LO2024
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…
math.LO2024
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…