Is it possible for infinite sets to exist in ZFC with the negation of the Axiom of Infinity?
135222
What are the consequences if Axiom of Infinity is negated?
119888
Is it possible to convert $\forall$ quantifiers to $\exists$ quantifiers without negation?
88736
How does the Axiom of Extensionality prove the uniqueness of Specified sets?
122947
What is the cardinality of the set of infinite cardinalities?
28452
Statement that is provable in $ZFC+CH$ yet unprovable in $ZFC+\lnot CH$
116135
A paradox related to computable reals?
100726
Prove that the set of powers of a set, $\{ A^n : n \in \mathbb{N} \}$ exists by using ZFC axioms (without replacement).
81509
The cardinality of a countable union of countable sets, without the axiom of choice
149673
Cardinality of an infinite union of finite sets
118189
Proving the pairing axiom from the rest of ZF
3902
Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
76974
What ZF axioms does Cantor's diagonal argument require?
47697
Russell's paradox: a set cannot contain its own powerset
113863
The non-existence of non-principal ultrafilters in ZF
272
Cantor Sets/nonempty/cardinality
144787
Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$
156252
Are sets constructed using only ZF measurable using ZFC?