48 research outputs found
Evolving Computability
We consider the degrees of non-computability (Weihrauch degrees) of finding
winning strategies (or more generally, Nash equilibria) in infinite sequential
games with certain winning sets (or more generally, outcome sets). In
particular, we show that as the complexity of the winning sets increases in the
difference hierarchy, the complexity of constructing winning strategies
increases in the effective Borel hierarchy.Comment: An extended abstract of this work has appeared in the Proceedings of
CiE 201
The descriptive theory of represented spaces
This is a survey on the ongoing development of a descriptive theory of
represented spaces, which is intended as an extension of both classical and
effective descriptive set theory to deal with both sets and functions between
represented spaces. Most material is from work-in-progress, and thus there may
be a stronger focus on projects involving the author than an objective survey
would merit.Comment: survey of work-in-progres
Searching for An Analogue of ATR_0 in the Weihrauch Lattice
3siThere are close similarities between the Weihrauch lattice and the zoo of axiom systems in reverse mathematics. Following these similarities has often allowed researchers to translate results from one setting to the other. However, amongst the big five axiom systems from reverse mathematics, so far has no identified counterpart in the Weihrauch degrees. We explore and evaluate several candidates, and conclude that the situation is complicated.openopenKihara T.; Marcone A.; Pauly A.Kihara, T.; Marcone, A.; Pauly, A