Effective Borel measurability and reducibility of functions

Weihrauch-completeness for layerwise computability

Layerwise computability is an effective counterpart to continuous functions that are almosteverywhere defined. This notion was introduced by Hoyrup and Rojas [17]. A function defined on Martin-Löf random inputs is called layerwise computable, if it becomes computable if each input is equipped with some bound on the layer where it passes a fixed universal Martin-Löf test. Interesting examples of...

The effective theory of Borel equivalence relations

The study of Borel equivalence relations under Borel reducibility has developed into an important area of descriptive set theory. The dichotomies of Silver ([19]) and Harrington-Kechris-Louveau ([5]) show that with respect to Borel reducibility, any Borel equivalence relation strictly above equality on ω is above equality on P(ω), the power set of ω, and any Borel equivalence relation strictly ...

Five-value rich lines‎, ‎Borel directions and uniqueness of meromorphic functions

For a meromorphic function $f$ in the complex plane, we shall introduce the definition of five-value rich line of $f$, and study the uniqueness of meromorphic functions of finite order in an angular domain by involving the five-value rich line and Borel directions. Finally, the relationship between a five-value rich line and a Borel direction is discussed, that is, every Borel direction of $f$ ...

A Wadge hierarchy for second countable spaces

Wadge reducibility provides a rich and nice analysis of Borel sets in Polish zero dimensional spaces. However, outside this framework, reducibility by continuous functions was shown to be ill behaved in many important cases. We define a notion of reducibility for subsets of a second countable T0 topological space based on the notions of admissible representations and relatively continuous relat...

An Analysis of the Lemmas of Urysohn and Urysohn-Tietze According to Effective Borel Measurability