Uncoutable set minus a countable subset is uncountable without axiom of choice or continuum hypothesis
3902
Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
93389
Uncountable sets of Hausdorff dimension zero
73350
Geometric solution to find a Set of totally ordered Subsets of $ \mathbb{N} $ is uncountable
99599
Uncountable and countable
32081
The dual version of trichotomy of cardinality without AC
99478
countably infinite union of countably infinite sets is countable
76809
"Some" and "Any"; countables and uncountable
88099
Not $\sigma$-compact set without axiom of choice
65308
Axiom of Choice: Family of non-empty sets mutually disjoint or not?
41937
Can one construct a non-measurable set without Axiom of choice?
28539
Does any uncountable set contain two disjoint uncountable sets?
156335
Proving Power Set of $\mathbb N$ is Uncountable
19297
Is the cofinite topology on an uncountable set first countable?
66301
The cardinality of the set of countably infinite subsets of an infinite set
60678
Does 'A countable infinite Cartesian product of countable sets is not necessarily countable' violate induction principle?
117133
Is there an infinite countable $\sigma$-algebra on an uncountable set
21431
The set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable?