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Results tagged with descriptive-set-theory
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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 descriptive set theory.
25
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2
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Writing a function on $\mathbb{R}$ as a sum of two injections
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function. It is well-known that, using transfinite recursion with a well-ordering of $\mathbb{R}$, one can construct two injective functions $g,h: \mat …
- 4,275
4
votes
1
answer
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Equality of Borel sets
I would like to understand the complexity of "equality of Borel sets". By complexity, I mean the complexity in the sense of Borel reducibility.
Of course, since there is no standard Borel space of Bo …
- 4,275
7
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answers
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A jump operator for Borel equivalence relations
It is well-known that with respect to Borel reducibility the class of Borel equivalence relations on a standard Borel space does not admit a maximal element. We can use the well-known Friedman-Staley …
- 4,275