F. Stephan

activity

20162022

collaborators

Showing math.LOShow all

6 papers · 1 filter

math.LO2020

members of thin $Π_{1}^{0}$ classes and generic degrees

Frank Stephan, Guohua Wu, Bowen Yuan

A $Π_{1}^{0}$ class $P$ is thin if every $Π_{1}^{0}$ subclass $Q$ of $P$ is the intersection of $P$ with some clopen set. In 1993, Cenzer, Downey, Jockusch and Shore initiated the…

math.LO2019

On the order dimension of locally countable partial orderings

Kojiro Higuchi, Steffen Lempp, Diip Raghavan +1

We show that the order dimension of the partial order of all finite subsets of $κ$ under set inclusion is $lo g_{2} (lo g_{2} (κ))$ whenever $κ$ is an infinite cardinal. We also…

math.LO2019

Randomness and initial segment complexity for probability measures

Andre Nies, Frank Stephan

We study algorithmic randomness properties for probability measures on Cantor space. We say that a measure $μ$ on the space of infinite bit sequences is ML absolutely continuous if…

math.LO2018

Subrecursive Approximations of Irrational Numbers by Variable Base Sums

Ivan Georgiev, Lars Kristiansen, Frank Stephan

There are numerous ways to represent real numbers. We may use, e.g., Cauchy sequences, Dedekind cuts, numerical base-10 expansions, numerical base-2 expansions and continued fracti…

math.LO2017

Covering the recursive sets

Bjørn Kjos-Hanssen, Frank Stephan, Sebastiaan A. Terwijn

We give solutions to two of the questions in a paper by Brendle, Brooke-Taylor, Ng and Nies. Our examples derive from a 2014 construction by Khan and Miller as well as new direct c…