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Results tagged with descriptive-set-theory
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user 1946
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.
92
votes
3
answers
14k
views
Is every sigma-algebra the Borel algebra of a topology?
This question arises from the excellent question posed on math.SE
by Salvo Tringali, namely, Correspondence
between Borel algebras and topology.
Since the question was not answered there after some ti …
- 236k
49
votes
0
answers
3k
views
Concerning proofs from the axiom of choice that ℝ³ admits surprising geometrical decompositi...
This question follows up on a comment I made on Joseph O'Rourke's
recent question, one of several questions here on mathoverflow
concerning surprising geometric partitions of space using the axiom
of …
- 236k
24
votes
2
answers
1k
views
What is the complexity of the winning condition in infinite Hex? In particular, is infinite ...
Consider the game of infinite Hex, where two players Red and Blue alternately place their stones on the infinite hex grid, each aiming to create a winning configuration.
Red wins after infinite play, …
- 236k
13
votes
1
answer
746
views
Is there a class of mathematical structures with non-isomorphic natural representations as a...
Background. The field of Borel equivalence relation theory
provides a robust, unifying theory that organizes most of the
classification problems of classical mathematics into a hierarchy,
allowing us …
- 236k
9
votes
1
answer
603
views
Does every cofinal branch through Kleene's O compute true arithmetic?
My question concerns cofinal branches through Kleene's $O$, which is a set of natural numbers and a computably enumerable relation $<_O$ on this set that provides
ordinal denotations for any desired c …
- 236k