Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with continuum-hypothesis
Search options answers only
not deleted
user 70618
Questions about the continuum hypothesis, or where the continuum hypothesis or its negation plays a role. This tag is also suitable, by extension, to refer to the generalized continuum hypothesis and related issues.
26
votes
Unnecessary uses of the Continuum Hypothesis
Theorem: The space $\mathbb N^*$ of non-principal ultrafilters on $\mathbb N$ is not homogeneous.
Using CH, it is fairly straightforward to prove there is a special kind of ultrafilter called a $P$-po …
9
votes
Uniqueness results that follow from CH
Here's one about my favorite topological space, the Stone–Čech remainder of the natural numbers, denoted $\mathbb N^*$ or $\omega^*$. The characterization is due to Parovicenko.
Assuming CH, $\mathbb …
14
votes
Accepted
Can the cardinal $2^{\aleph_0}$ be order-embedded in ${\cal P}(\omega)/(\text{fin})$?
Yes! The fact that this is consistent is originally due to Laver. Later, Baumgartner, Frankiewicz, and Zbierski strengthened Laver's result to the following theorem:
Theorem: Is it consistent that $\m …
- 18.5k
9
votes
Accepted
The Parovichenko cardinal, is it equal to $\max\{\aleph_2,\mathfrak p\}$?
No -- it is consistent that $\mathsf{CH}$ fails, and that every compact Hausdorff space of weight $\leq\!\mathfrak{c}$ is a continuous image of $\beta \mathbb N \setminus \mathbb N$. (This is due to B …
- 18.5k
8
votes
Accepted
Uniformization of almost disjoint families
No, this is not consistent: there is (provably in ZFC) an almost disjoint family of size $\aleph_1$ and a two-valued function on that family such that the function cannot be uniformized in the way you …
- 18.5k
20
votes
Accepted
Is $[0,1]$ a disjoint union of $\aleph_1$ compact subsets with empty interior?
It is independent of ZFC. As you mention, CH implies the answer is yes. A different axiom, MA+$\neg$CH, implies the answer is no.
A little more precisely, there is a cardinal number denoted $\mathrm{ …
- 18.5k
11
votes
Is it still an open problem whether $\mathbb{R}^\omega$ is normal in the box topology?
I'm transcribing here some things from the comments section, so that this question can be marked as answered:
The problem is still open.
This survey by Roitman and Williams, from 2015, said that it wa …