axiom of choice is equivalent to "the product of nonempty collection of nonempty sets is nonempty"
62936
Proving equivalencies of two versions of the Axiom of Choice
13661
Axiom of Regularity allows for this set be an element of itself
118189
Proving the pairing axiom from the rest of ZF
140868
Axiomatization of $\mathbb{Z}$ via well-ordering of positives.
50506
What concept does an open set axiomatise?
109054
Given an infinite set of cardinality $X$, is there a chain in $\mathcal P(X)$ of the same cardinalty of $\mathcal P(X)$?
78117
Closed property of nonempty finite set
58447
Is axiom of choice required for there to be an infinite linearly independent set in a (non-finite-dimensional) vector space?
139992
Is power-associativity finitely axiomatizable?
60678
Does 'A countable infinite Cartesian product of countable sets is not necessarily countable' violate induction principle?
155207
Confusion regarding one formulation of the Axiom of Choice.
136755
Direct proof of empty set being subset of every set
89506
Union of disjoint sets : Equivalence relations
98580
Lebesgue-measurable sets requiring the Axiom of Choice to construct
61747
Proof of exchange principle in set theory
150385
The use of the Axiom of Choice in this proof of the sequence lemma
5313
Existence of how many sets is asserted by the axiom of choice in this case?