Countable set of finite sets is countable (without the axiom of choice).
41365
Choice function for collection of arbitrary finite sets. AC required?
120562
If A is an infinite set and B is at most countable set, prove that A and $A \cup B$ have the same cardinality
94413
Proving Dedekind finite implies finite assuming countable choice
31509
Is axiom of choice necessary for proving that every infinite set has a countably infinite subset?
2403
Can a countable set contain uncountably many infinite subsets such that the intersection of any two such distinct subsets is finite?
98151
Suppose that A is a countable set. Show that the set B is also countable if there is an onto function f from A to B.
68230
The cardinality of a countable union of sets with less than continuum cardinality
78290
Countable axiom of choice: why you can't prove it from just ZF
66301
The cardinality of the set of countably infinite subsets of an infinite set
102543
Real definition of "countable set"
5313
Existence of how many sets is asserted by the axiom of choice in this case?
12436
The cardinality of the set of all finite subsets of an infinite set
149673
Cardinality of an infinite union of finite sets
70143
Mutually exclusive countable subsets of a countable set
91163
Let the set S be infinite, and the set T countably infinite. Show that S and S U T have the same cardinality
32774
Finite Cartesian Product of Countable sets is countable?
53025
Why the need of Axiom of Countable Choice?