Munkres lemma 13.1 and Axiom of Choice
33563
Is the axiom of choice used in the proof that every open set is the union of basis elements (Mukres, Lemma 13.1)
29744
Compactness and axiomatisability
31389
consistency of ZF\{Power Set axiom}
127886
Artin's lemma and some morphisms.
87451
Construction of matrices under ZFC axioms
104771
Dedekind's cut and axioms
9158
Proving that a propositional theory of any cardinality has an independent set of axioms
27899
Can we prove the existence of $A\cup B$ without the union axiom?
113863
The non-existence of non-principal ultrafilters in ZF
19414
Uncountable subset with uncountable complement, without the Axiom of Choice
88595
Prob. 21, Sec. 17 in Munkres' TOPOLOGY, 2nd ed: Closure and complementation can result in at most 14 different sets
98580
Lebesgue-measurable sets requiring the Axiom of Choice to construct
142315
How does the Axiom of Regularity apply to $A=\{1,2,3\}$?
140868
Axiomatization of $\mathbb{Z}$ via well-ordering of positives.
153634
A statment about the equivalence between the Axiom of Choice and the surjectivity of the projections.
48615
Does the assertion that every two cardinalities are comparable imply the axiom of choice?
131889
Axiom of choice and calculus