If a set theory allowed the existence of $x\cup y$, would that imply the existence of $\cup S$?
55564
Can the union axiom be weakened?
107383
Derived sets - prove $(A \cup B)' = A' \cup B'$
19396
For subspaces, if $N\subseteq M_1\cup\cdots\cup M_k$, then $N\subseteq M_i$ for some $i$?
20004
Meta Theory when studying Set Theory
141299
Alternative set theories
49994
Deduction of $\forall y \exists x (x=y)$
10472
Is every set a subset?
78763
Prove that $ S=\{0\}\cup\left(\bigcup_{n=0}^{\infty} \{\frac{1}{n}\}\right)$ is a compact set in $\mathbb{R}$.
65371
Does $2^X \cong 2^Y$ imply $X \cong Y$ without assuming the axiom of choice?
47434
Proof that $A \subseteq B \Leftrightarrow A \cup B = B$
10909
$|A \cup B| = \mathfrak{c}$, then $A$ or $B$ has cardinality $\mathfrak{c}$.
144899
Do We Need the Axiom of Choice for Finite Sets?
112731
If $Y$ is connected, why is $A\cup Y$ connected in this case?
111723
Can it be proven in $\sf ZF^{\neg\infty}$ that the sets $x_n=\{x_{n+1}\}$ do not exist?
58186
Set theory proof, $\exists g(g\colon A\twoheadrightarrow C)$ or $\exists h(h\colon C\hookrightarrow B)$
58447
Is axiom of choice required for there to be an infinite linearly independent set in a (non-finite-dimensional) vector space?
18330
Does $R[x] \cong S[x]$ imply $R \cong S$?