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Results tagged with descriptive-set-theory
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user 109573
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.
11
votes
1
answer
367
views
Is $V=L$ equivalent to there being a $\Sigma_1$ well-ordering of the universe?
Working in ZF, it's well-known that for any $n \ge 2,$ the claim that there is a $\Sigma_n$ well-ordering of the universe is equivalent to the axiom $V=HOD.$ It seems natural to believe there should b …
- 4,316
11
votes
Accepted
How much choice is necessary to prove this statement?
Your statement is equivalent to the assertion that there is a function choosing an enumeration of every countable ordinal. From an enumeration of $\alpha,$ you can easily inject it into a countable se …
- 4,316
4
votes
Accepted
Strong form of $\mathtt{PSP}$ for $K_\sigma$ sets
Here's a counterexample. Let $X$ be the set of bounded sequences, and let $A$ be the set of sequences which have only finitely many nonzero terms and achieve a strict maximum at the last nonzero term. …
- 4,316