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Pincherle's theorem in Reverse Mathematics and computability theory
Dag Normann, Sam Sanders
We study the logical and computational properties of basic theorems of uncountable mathematics, in particular Pincherle's theorem, published in 1882. This theorem states that a loc…
Reverse Mathematics of topology: dimension, paracompactness, and splittings
Sam Sanders
Reverse Mathematics (RM hereafter) is a program in the foundations of mathematics founded by Friedman and developed extensively by Simpson and others. The aim of RM is to find the…
Some nonstandard equivalences in Reverse Mathematics
Sam Sanders
Reverse Mathematics (RM) is a program in the foundations of mathematics founded by Friedman and developed extensively by Simpson. The aim of RM is finding the minimal axioms needed…
A note on non-classical Nonstandard Arithmetic
Sam Sanders
Recently, a number of formal systems for Nonstandard Analysis restricted to the language of finite types, i.e. nonstandard arithmetic, have been proposed. We single out one particu…
Splittings and disjunctions in Reverse Mathematics
Sam Sanders
Reverse Mathematics (RM hereafter) is a program in the foundations of mathematics founded by Friedman and developed extensively by Simpson and others. The aim of RM is to find the…
A footnote to The crisis in contemporary mathematics
Boris Katz, Mikhail G. Katz, Sam Sanders
We examine the preparation and context of the paper "The Crisis in Contemporary Mathematics" by Errett Bishop, published 1975 in Historia Mathematica. Bishop tried to moderate the…