Descriptive Set Theory is the study of definable subsets of Polish spaces, where definable is taken to mean from the Borel or projective hierarchies. Other topics include infinite games and determinacy, definable equivalence relations and Borel reductions between them, Polish groups, and effective ...

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Related Open Game in Analytic Determinacy

For this question, please refer to Chapter 33 page 638, Set Theory Millennium Edition, by Thomas Jech. The proof of analytic games $G_A$ is converted into an open game $G^\ast$ on some suitable ...
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Non Borel sets without axiom of choice

This is a simple doubt of mine about the basics of measure theory, which should be easy for the logicians to answer. The example I know of non Borel sets would be a Hamel basis, which needs axiom of ...
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disjoint translates of a dense uncountable set

If {c(n)} is an arbitrary sequence of irrational numbers converging to 0 then Q + c(n), the set obtained by adding c(n) to the set of rational numbers Q, is clearly disjoint from Q for each n. Is ...
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A subset of Baire space Wadge incomparable to a Borel set?

Let $\omega^\omega$ be Baire space. If $A,B\subseteq\omega^\omega$ we say that $A$ is Wadge reducible to $B$ (written $A\leq_w B$) if there is a continuous function ...