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Results tagged with set-theory
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user 43954
forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.
2
votes
Accepted
What is the smallest density of a metrizable space without countable separation?
Since this problem has an affirmative answer, the last question should have a negative answer and then the smallest density of the space in the first question can be $\frak c^+$.
- 5,409
5
votes
1
answer
319
views
Bounds for a small cardinal
$\newcommand{\w}{\omega}\newcommand{\F}{\mathcal F}\newcommand{\I}{\mathcal I}\newcommand{\J}{\mathcal J}\newcommand{\M}{\mathcal M}\newcommand{\N}{\mathcal N}\newcommand{\x}{\mathfrak x}\newcommand{\ …
- 5,409
3
votes
1
answer
162
views
Bounds for a covering number of the circle group $\mathbb T$ by some its small subgroups
$\newcommand{\w}{\omega}\newcommand{\A}{\mathcal A}\newcommand{\F}{\mathcal F}\newcommand{\I}{\mathcal I}\newcommand{\J}{\mathcal J}\newcommand{\M}{\mathcal M}\newcommand{\N}{\mathcal N}\newcommand{\x …
- 5,409
11
votes
Accepted
Non meager rectangle
I pointed this question to Taras Banakh,
who pointed to me his joint paper with Lyubomyr Zdomskyy “Non-meager free sets for meager relations on Polish spaces” which contains an answer.
Abstract. We …
- 5,409
3
votes
Accepted
Does a continuous map from $\kappa^\omega$ to $[0,1]^\omega$ have a non-scattered fiber?
The continuity of $f$ is not needed. Indeed, suppose to the contrary that $\kappa^\omega$ is a union of the family $\{F_\alpha:\alpha<\frak c\}$ of fibers of $f$. Let $\alpha<\frak c$ be any index. Si …
- 5,409
7
votes
Accepted
The cardinal characteristic $\mathfrak r_{(X,f)}$ of a dynamical system
Unfortunately, $\mathfrak r_{(2^\omega,f)}\ge\mathfrak r$. Indeed, let $\mathcal R$ be a family of infinite subsets of $\omega$ such that $|\mathcal R|=\mathfrak r_{(2^\omega,f)}$ and for any $x=(x_n) …
- 5,409