Zermelo set theory and Zorn's lemma
115675
Strange consequences of Axiom of Choice in Zermelo set theory
120273
Showing that a collection of sets is a $\sigma$-algebra: either set or complement is countable
3663
Finding counterexamples in elementary set theory.
116378
Nonhomeomorphic subsets of the plane
32441
How to prove or disprove statements about sets
6088
Theorem of Arzelà-Ascoli
42095
Existence in ZF of a set with countable power set
130771
Sets and the principle of inclusion and exclusion
155890
Does Bezout's lemma work both ways.
33563
Is the axiom of choice used in the proof that every open set is the union of basis elements (Mukres, Lemma 13.1)
16796
Zermelo-Fraenkel set theory and Hilbert's axioms for geometry
18364
When does the set enter set theory?
29668
Why doesn't Zorn's lemma apply to $[0,1)$?
39708
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
69724
Is Zorn's lemma necessary to show discontinuous $f\colon {\mathbb R} \to {\mathbb R}$ satisfying $f(x+y) = f(x) + f(y)$?
142631
Show that A has the same cardinality as $A\setminus\{x,y,z\}$
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set