Is this an equivalent form of Axiom of Choice?
60903
Injection of union into disjoint union
12539
Set Theory: Equivalency of Axiom of Choice and Choice Function
950
Doubts on the axiom of union?
130998
Is $\exists x \in A ~:~ P(x)$ the same as $\exists x ~:~ x \in A \implies P(x)$
77548
Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?
142840
Open axioms of equality
81509
The cardinality of a countable union of countable sets, without the axiom of choice
48615
Does the assertion that every two cardinalities are comparable imply the axiom of choice?
29744
Compactness and axiomatisability
155207
Confusion regarding one formulation of the Axiom of Choice.
142219
Does the splitting lemma hold without the axiom of choice?
153634
A statment about the equivalence between the Axiom of Choice and the surjectivity of the projections.
19414
Uncountable subset with uncountable complement, without the Axiom of Choice
17624
Axiom of Choice iff Every set has a choice function
25187
Why $∀x(P(x)→Q)$ is equivalent to $∃xP(x)→Q$
25997
Conditions Equivalent to Injectivity
45623
Axiom of Choice: What exactly is a choice, and when and why is it needed?