Are there an uncountable subset of $\mathcal{P}(\mathbb{N})$ such that it has total order under the subset relation?
91485
Finding an uncountable chain of subsets the integers
150605
Existence of a regular uncountable $\aleph_{\alpha}$ without $\mathsf{AC}$
39880
Cardinality of Orderings of $\mathbb{R}$
121860
Number of well-ordering relations on a well-orderable infinite set $A$?
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
139078
Infinite partition of $\mathbb N$ by infinite subsets
14972
Cardinality of Vitali sets: countably or uncountably infinite?
117133
Is there an infinite countable $\sigma$-algebra on an uncountable set
119886
The cantor set is uncountable
124060
Are these subsets of the powerset P(N) countable?
145471
$\Gamma \subset \mathbb{R}^{+}$ is uncountable. Can we choose a sequence from $\Gamma$ of which the sum is $\infty$
19297
Is the cofinite topology on an uncountable set first countable?
67064
Uncountable minus countable set is uncountable
63276
Is an arbitrary union of a chain of countable sets countable?
35692
The set of all finite subsets of the natural numbers is countable
70143
Mutually exclusive countable subsets of a countable set
22391
Is the set of all pairs of real numbers uncountable?