7 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…