# 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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### A Baire space with meager projections

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### Is a Borel image of a Polish space analytic?

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### Countable network vs countable Borel network

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### Arithmetic sums of Marczewski null sets

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### A strong plus-one hypothesis

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### Base zero-dimensional spaces

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### reverse mathematics of the Lebesgue measurability of analytic sets

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### Is it known how the Sigma Algebra generated by Jordan measurable sets compares to universally measurable sets and analytic sets?

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### Support of a regular measure Reg

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### $\Delta^{1}_{2}$ and degrees of constructibility $\textbf{on sets}$

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### Completely I-non-measurable unions in Polish spaces

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### Can $\Delta^{1}_{2}$ separate degrees of constructibility?

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### Can we inductively define Wadge-well-foundedness?

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### Separation principle in generic models?

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### How much can complexities of bases of a “simple” space vary?

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### Differences between the reduced Borel field and the category algebra of a space

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### Characterizing compact Hausdorff spaces whose all subsets are Borel

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### Interpreting a space in Baire space: how many facts do I need to understand the whole thing?

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### When can I “draw” a topology in Baire space?

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### Topologically Ordered Families of Disjoint Cantor Sets in $I$?

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### Can an injective $f: \Bbb{R}^m \to \Bbb{R}^n$ have a closed graph for $m>n$?

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### Co-cones in the Turing degrees

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### A connected Borel subgroup of the plane

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### A commuting pair of functions with no common bijective part

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### Closed balls vs closure of open balls

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### How (non-)computable is set theory?

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### Nice representation of open sets in $\sigma$-algebras in certain circumstances

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### Nice arrangement of open sets in $\sigma$-algebras

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### ZF + “every Suslin set of reals is ${\bf \Sigma}^1_2$”

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### Borel class of multivalued mapping

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### An example of a Borel map of the first class

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### Example of a Baire Class $1$ function $f$ satisfying $\omega\cdot n<\beta(f)\leq \omega\cdot (n+1)$ for some natural number $n\geq 1.$

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### Examples of Baire Class $\xi+1$ but not $\xi$ functions for each countable ordinal $\xi.$

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### Is there a model of set theory in which $\mathfrak p< \mathfrak b < \mathfrak q$?

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### Reference Request: Existence of Ordinal Rank Theory?

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### Class of Borel mapping of multivalued map

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### Automorphisms of power set lattice mod finite

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### Measurably-isomorphic subsets of polish spaces and the continuum hypothesis

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### The Axiom of Determinacy and the Banach-Mazur game

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### A version of the Martin–Solovay tree for $H_\kappa$

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### Countable $\mathbf\Sigma^1_2$ equivalence relations

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### A kind of 0-1 law?

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### A strange planar set and the Continuum Hypothesis

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### Is there a first-countable space containing a closed discrete subset which is not $G_\delta$?

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### Is a locally finite union of $G_\delta$-sets a $G_\delta$-set?

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### Equivalent of Lusin's Theorem in Borel setting

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### The Fubini property of the $\sigma$-ideal generated by closed subsets of measure zero

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### Can the Turing degrees be linearly ordered?

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### On the topological complexity of the set of winning strategies for Gale-Stewart Games

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