26 citations · 30 across the 10 of their papers we have counts for
12 papers
Intersections of spaces in the Borel hierarchy
Vassilios Gregoriades
We show that if is one of the spaces , , or where , and the Fréchet space $\textstyle \bigcap…
On a Question of Jaegers
Vassilios Gregoriades
We show that there exists a positive arithmetical formula , where , , with no hyperarithmetical fixed point. This answers a question of Gerhard Jäge…
Uniformity results on the Baire property
Vassilios Gregoriades
We are concerned with the problem of witnessing the Baire property of the Borel and the projective sets (assuming determinacy) through a sufficiently definable function in the code…
The Dyck and the Preiss separation uniformly
Vassilios Gregoriades
We are concerned with two separation theorems about analytic sets by Dyck and Preiss, the former involves the positively-defined subsets of the Cantor space and the latter the Bore…
Choice free Fixed Point Property in separable Banach spaces
Vassilios Gregoriades
We show that the standard approach of minimal invariant sets, which applies Zorn's Lemma and is used to prove fixed point theorems for non-expansive mappings in Banach spaces can b…
Classes of Polish spaces under effective Borel isomorphism
Vassilios Gregoriades
We study the equivalence classes under isomorphism, otherwise effective-Borel isomorphism, between complete separable metric spaces which admit a recursive presentation and…
One more recursive-theoretic characterization of the Topological Vaught Conjecture
Vassilios Gregoriades
We prove in ZF a recursive-theoretic characterization of the Topological Vaught Conjecture by revisiting the fact that orbits in Polish -spaces are Borel sets.
Turing degrees in Polish spaces and decomposability of Borel functions
Vassilios Gregoriades, Takayuki Kihara, Keng Meng Ng
We give a partial answer to an important open problem in descriptive set theory, the Decomposability Conjecture for Borel functions on an analytic subset of a Polish space to a sep…
A comparison of concepts from computable analysis and effective descriptive set theory
Vassilios Gregoriades, Tamás Kispéter, Arno Pauly
Computable analysis and effective descriptive set theory are both concerned with complete metric spaces, functions between them and subsets thereof in an effective setting. The pre…
Turning Borel sets into clopen sets effectively
Vassilios Gregoriades
We present the effective version of the theorem about turning Borel sets in Polish spaces into clopen sets while preserving the Borel structure of the underlying space. We show tha…
The descriptive set-theoretic complexity of the set of points of continuity of a multi-valued function
Vassilios Gregoriades
In this article we treat a notion of continuity for a multi-valued function and we compute the descriptive set-theoretic complexity of the set of all for which is conti…
The descriptive set-theoretic complexity of the set of points of continuity of a multi-valued function (Extended Abstract)
Vassilios Gregoriades
In this article we treat a notion of continuity for a multi-valued function F and we compute the descriptive set-theoretic complexity of the set of all x for which F is continuous…