Skip to main content

All Questions

7 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
8 votes
0 answers
241 views

Topological applications of $\mathfrak{p}=\mathfrak{t}$

I'm working on the Malliaris-Shelah's recent result of $\mathfrak{p}=\mathfrak{t}$, but I'm more interested in what possible topological applications can derivate from this equality. Searching in ...
Alexei0709's user avatar
8 votes
0 answers
226 views

When can we force two frames to be homeomorphic?

Recall that if $M,N$ are two structures of the same type, then $M$ is $\mathcal{L}_{\infty,\omega}$ elementarily equivalent to $N$ precisely when $M$ and $N$ are isomorphic in some forcing extension. ...
Joseph Van Name's user avatar
5 votes
0 answers
102 views

Universal and strong $Q$-sets

A subset $X\subset \mathbb R$ is called $\bullet$ a $Q$-set if for every subset $A\subset X$ there exists a $\sigma$-compact set $C\subset\mathbb R$ such that $C\cap X=A$; $\bullet$ a strong $Q$-set ...
Taras Banakh's user avatar
  • 41.9k
4 votes
0 answers
142 views

Consistency of a strange (choice-wise) set of reals, pt. 2

This is a follow-up on this question. Consider a set $X\subseteq \mathbb{R}$ such that $X$ is not separable wrt its subspace topology Every countable family of non-empty pairwise disjoint subsets of $...
Lorenzo's user avatar
  • 2,286
4 votes
0 answers
161 views

Preservation of Baumgartner's I-ultrafilters under various forcings

For $I\subset \mathcal{P}(2^\omega)$, an ultrafilter $U$ on $\omega$ is said to be an I-ultrafilter if for all $f:\omega \to 2^\omega$, there exists $A\in U$ such that $f''[A]\in I$ [Baumgartner]. In ...
Jing Zhang's user avatar
  • 3,038
3 votes
0 answers
113 views

Hereditarily Lindelöf spaces with density continuum

Since there are L-spaces (provably in ZFC), under CH we have regular, hereditarily Lindelöf spaces with density continuum. However, I cannot find an example of such a space under not CH, nor a proof ...
GAW's user avatar
  • 31
3 votes
0 answers
88 views

Which spaces are still Lindelöf after forcing with a Suslin tree?

Let $T$ be a Suslin tree and $f:T\to Y$ be continuous. ($T$ is endowed with the order topology.) Assume that the image of $T$ is contained in a Lindelöf subset of $Y$. Then, force with $T$. Which ...
Mathieu Baillif's user avatar