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Results tagged with descriptive-set-theory
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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.
6
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A simpler proof that compact sets have cardinality continuum?
Is there a simple reason why uncountable compact sets of real numbers have cardinality continuum?
I know that this is immediate from the Cantor-Bendixon Theorem, but I wonder whether this consequence …
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11
votes
1
answer
424
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A classic cardinal characteristic of the continuum in disguise?
We believe the answer to the following question, that is relevant to a joint research project with Piotr Szewczak, should be known. We would appreciate any help or pointer.
Needed definitions may be f …
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6
votes
1
answer
969
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A property of the Frechet filter and every ultrafilter
(Joint question with Piotr Szewczak.)
Definitions and notation. By filter we mean a filter on $\omega$ containing the cofinite sets at least.
For a filter $\mathcal{F}$, let $\mathcal{F}^+:=\{A\subs …
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4
votes
1
answer
337
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Almost compact sets
Update:
Q1 is answered in the comments.
I think that the usual arguments show that every relatively almost compact set in a space is closed in the space.
Original question:
A set $K$ in a space $X …
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5
votes
1
answer
136
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Is it consistent that the additivity of Lebesgue null sets is greater than $\frak h$?
This question concerns combinatorial cardinals of the continuum.
Some of these are listed in the following diagram, from Blass's survey on the topic.
There are some additional cardinals, related to a …
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8
votes
2
answers
748
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Avoiding countable subgroups of general uncountable groups
The following problem is a general form of another problem (motivation is available there). Initially, the problems were posted together, but the first one is solved below, a solution that does not ap …
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9
votes
1
answer
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The cardinality of projections of subsets of the Hilbert cube by inner products
I have three related questions.
Question 1: Is there a subset $X$ of the Hilbert cube $[0,1]^{\Bbb N}$ of cardinality continuum, such that for each sequence $a\in [0,1]^{\Bbb N}$ with $\sum a_n$ finit …
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