If $X$ is well-ordered set, how to prove that $\mathcal{P}(X)$ can be linearly ordered?
72104
Totally ordering the power set of a well ordered set.
144693
Show that if $B \subseteq C$, then $\mathcal{P}(B) \subseteq \mathcal{P}(C)$
62977
Show on $\mathbb{N}$ there are $2^{\aleph_0}$ nonisomorphic linear orders.
49621
Proof of "well-founded iff there is no sequence $x_n$ s.t. $(x_{n+1}, x_n) \in R$"
146062
A "Cantor-Schroder-Bernstein" theorem for partially-ordered-sets
63489
The class of cardinal numbers is well ordered
19924
Uncountable ordinals without power set axiom
134859
Let $(X, \mathcal{T})$ be a metrizable space. Prove that $X$ Lindelöf implies that $X$ is separable.
154578
Proving there is a sequence convergent to a limit point of a set without axiom of countable choice?
150385
The use of the Axiom of Choice in this proof of the sequence lemma
114550
Well-ordering theorem and second-order logic
101986
Prob. 2, Sec. 20 in Munkres' TOPOLOGY, 2nd ed: The dictionary order topology on $\mathbb{R} \times \mathbb{R}$ is metrizable.
37915
$\sqrt{2}$ is irrational proof using well-Ordering Property
105791
Does separability imply the Lindelöf property?
112049
How many elements does $\mathcal{P}(A)$ have?
55978
Prove that for every countable ordinal $\alpha$, $\alpha\times[0,1)$ is order isomoprhic to $[0,1)$
121860
Number of well-ordering relations on a well-orderable infinite set $A$?