Prove that there is no set $\Omega$ such that $(\forall A)(A \subseteq \Omega)$
13374
Why is "the set of all sets" a paradox, in Layman's terms?
112008
Ordinal $\omega_1$ is not compact
80916
How to prove that if $A\subseteq A\times A$, then $A=\varnothing$?
146560
Is there any uncountably infinite set that does not generate the reals?
157513
How can I prove that these sets are countable infinite?
62208
If $A$ is a non-empty set, then $A \notin A$
148516
Proof that $\omega^\omega$ is completely metrizable and second countable
31212
The existence of the empty set is an axiom of ZFC or not?
100726
Prove that the set of powers of a set, $\{ A^n : n \in \mathbb{N} \}$ exists by using ZFC axioms (without replacement).
59275
If $X$ is an infinite set, then $X$ with the discrete topology is not compact
37183
Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
125411
Infinite set always has a countably infinite subset
157218
If $E\subseteq X$ is connected, $E\cap A\neq\emptyset$ and $E\cap(X\setminus A)\neq\emptyset$ then $E\cap\partial A\neq\emptyset$
90826
Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly
272
Cantor Sets/nonempty/cardinality
10472
Is every set a subset?
154230
In $\mathsf{ZF}$, for each set $A$ exists an ordinal $\alpha$ such that no surjection $A\to \alpha$ exists