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math.NT2024
Improved lower bounds for strong -conjectures
Rupert Hölzl, Sören Kleine, Frank Stephan
The well-known -conjecture concerns triples of non-zero integers that are coprime and satisfy . The strong -conjecture is a generalisation to summa…
math.LO2024
Independence and Induction in Reverse Mathematics
David Belanger, Chi Tat Chong, Rupert Hölzl +1
We continue the project of the study of reverse mathematics principles inspired by cardinal invariants. In this article in particular we focus on principles encapsulating the exist…
math.LO2024
Randomness versus superspeedability
Rupert Hölzl, Philip Janicki, Wolfgang Merkle +1
Speedable numbers are real numbers which are algorithmically approximable from below and whose approximations can be accelerated nonuniformly. We begin this article by answering a…