# Questions tagged [descriptive-set-theory]

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.

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### Non-compact dynamical systems

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### Topological proof that a Vitali set is not Borel

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### Locally compact Polish groups acting on standard Lebesgue spaces

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### Does every cofinal branch through Kleene's O compute true arithmetic?

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### Analyzing my definition of Average which uses a variation of the Lebesgue Integral and Measure [closed]

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### Is there a simple proof that proves $C^1[0, 1]$ is $\Sigma^1_1$ in $C[0, 1]$?

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### Function whose graph is a Borel relation

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### Borel hierarchy and tail sets

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### Lambda system generated by a non-atomic collection

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### Is the co-projection of the projection of a Borel set Lebesgue measurable?

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### Pointwise definable models of determinacy

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### Reference for Borel $\sigma$-algebra of topology of convergence in probability

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### When is validity definable in $L_\alpha$?

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### The measure of ideals generated by random reals

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### Borel rank collapse in Hilbert cube modulo $\sigma$-ideal generated by zero-dimensional sets

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### Detecting comprehension topologically

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### Definition of random measures

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### Kurtz randomness and supermartingales with infinite *limit*

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### Does $Π^1_{2n+1} = (Σ^1_{2n+1})^{M_{2n-1}}$?

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### General theory of the reals in Solovay-like models

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### Undetermined Banach-Mazur games in ZF?

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### Suslin representation of sets and limits to Shoenfield's Absoluteness

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### Improving a Lindstrom-y fact about $\mathcal{L}_{\omega_1,\omega}$?

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### “Robinson arithmetic” for (some) levels of $L$?

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### When does “sufficient genericity” actually suffice?

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### Is there an almost strongly zero-dimensional space which is not strongly zero-dimensional

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### Question about additive subgroups of the real line and the density topology

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### Can it be that universal measurability is preserved by projections?

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### How much choice is required for a countably-infinite index subgroup of the real additive group?

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### Source on smooth equivalence relations under continuous reducibility?

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### Is the inverse of a measurably parametrised family of bijections between standard Borel spaces measurably parametrised?

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### Ramsey type properties of $F_\sigma$ ideals

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### The Borel class of a countable union of $G_\delta$-sets, which are absolute $F_{\sigma\delta}$

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### Borel / Wadge hierarchies on subsets closed under prepending a finite prefix

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### Uncountable disjoint closed coverings of $[0,1]$

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### Set of perfect subsets of a Borel set

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### Fraïssé Limit and Ultraproduct

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### Regularity properties of Turing-invariant and arbitrary sets of reals

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### Convergence and winning strategies

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### A slight extension of Sacks theorem

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### A partial relativization of Gandy's basis theorem

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### Variously pointed closed sets

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### Do the higher levels of the Borel hierarchy correspond to absolute topological properties?

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### Abstract transverse measure theory

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### Examples of independent $\Sigma_4^1$ statements

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### Nowhere Baire spaces

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### Product of Bernstein sets

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### Concerning Luzin-(N)-property

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### Is there a universally meager air space?

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