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15
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Does proving that closed subset of Polish space is Polish require axiom of countable choice?

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#solution-verification #axiom-of-choice #descriptive-set-theory #polish-spaces
61
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Writing down a formula for "X is meager" in second order arithmetic with low complexity

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#set-theory #descriptive-set-theory
154
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CH implies $\omega_1$ pairwise disjoint of perfect set

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#set-theory #descriptive-set-theory #transfinite-induction
83
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How can I write a perfect set as $c$ many pairwise disjoint perfect sets

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#set-theory #descriptive-set-theory #transfinite-recursion #transfinite-induction
63
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Borel $\boldsymbol{\Delta}^0_\alpha$ vs. $\bigcup_{\xi<\alpha}\boldsymbol{\Delta}^0_{\xi}$ for limit $\alpha$

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#set-theory #descriptive-set-theory
84
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Homeomorphic images of an "almost" basic open set in $2^{\omega}$

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#general-topology #set-theory #descriptive-set-theory
350
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Cantor-Bendixson Theorem -- Kechris' proof of perfectness

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#general-topology #descriptive-set-theory
204
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Is there a $\mathbb{Q}$-basis of $\mathbb{R}$ that is Borel?

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#linear-algebra #general-topology #measure-theory #set-theory #descriptive-set-theory
554
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Why does the Cantor-Bendixson cupcake theorem need transfinite induction?

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#general-topology #descriptive-set-theory #reverse-math
74
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Complexity of formulae involving projective sets in Polish spaces

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#logic #predicate-logic #descriptive-set-theory #descriptive-complexity
528
Views

There is a $\Sigma^1_1$ universal set and this is not Borel. Where did we use the axiom of choice?

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#set-theory #axiom-of-choice #descriptive-set-theory
115
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Borel hierarchy within Wadge hierarchy

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#reference-request #set-theory #descriptive-set-theory #infinite-games
124
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Continuous parametrization of continuous functions in the Baire space $\omega^\omega$

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#set-theory #solution-verification #descriptive-set-theory #the-baire-space
222
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Total disconnection and zero-dimension in Polish spaces

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#general-topology #descriptive-set-theory #polish-spaces
52
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Operation over the Baire space $\omega^\omega$ that preserves Borel sets

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#set-theory #descriptive-set-theory #borel-sets #the-baire-space

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