6 papers · 1 filter
On countability and representations
Sam Sanders
The topic of this paper is the subtle interplay between countability and representations. In particular, we establish that the definition of countability of a certain set cruci…
From real analysis to the sorites paradox via Reverse Mathematics
Walter Dean, Sam Sanders
This paper presents a reverse mathematical analysis of several forms of the sorites paradox. We first illustrate how traditional formulations are reliant on Hölder's Representatio…
Coding is hard
Sam Sanders
A central topic in mathematical logic is the classification of theorems from mathematics in hierarchies according to their logical strength. Ideally, the place of a theorem in a hi…
Sometimes tame, sometimes wild: weak continuity
Sam Sanders
Continuity is one of the most central notions in mathematics, physics, and computer science. An interesting associated topic is decompositions of continuity, where continuity is sh…
Connecting real and hyperarithmetical analysis
Sam Sanders
Going back to Kreisel in the Sixties, hyperarithmetical analysis is a cluster of logical systems just beyond arithmetical comprehension. Only recently natural examples of theorems…
A note on continuous functions on metric spaces
Sam Sanders
Continuous functions on the unit interval are relatively tame from the logical and computational point of view. A similar behaviour is exhibited by continuous functions on compact…