Is the axiom of countable choice needed for the proof of this special case of equivalence of limit definitions?
58631
Continuity and the Axiom of Choice
62936
Proving equivalencies of two versions of the Axiom of Choice
105815
Does proving (second countable) $\Rightarrow$ (Lindelöf) require the axiom of choice?
142045
What's the definition of limit of sets(esp. ordinals) in set theory?
102202
The smallest infinity and the axiom of choice
31509
Is axiom of choice necessary for proving that every infinite set has a countably infinite subset?
23442
Cardinality of the union of infinite and countable sets
27937
Cartesian Product of Two Countable Sets is Countable
9021
An infinite subset of a countable set is countable
88736
How does the Axiom of Extensionality prove the uniqueness of Specified sets?
148927
Why does every countable limit ordinal have cofinality $\omega$?
99478
countably infinite union of countably infinite sets is countable
120311
Equivalence of Axiom of Regularity
12539
Set Theory: Equivalency of Axiom of Choice and Choice Function
20252
The Axiom of Choice and the Cartesian Product.
109054
Given an infinite set of cardinality $X$, is there a chain in $\mathcal P(X)$ of the same cardinalty of $\mathcal P(X)$?
84936
The set of all finite sequences of members of a countable set is also countable