Existence of well-order on an arbitrary infinite set $X$ without a largest element
126569
Can we find a well ordering on an infinite set with no largest element?
33008
Linear order where every initial segment is finite
9021
An infinite subset of a countable set is countable
42314
Without appealing to choice, can we prove that if $X$ is well-orderable, then so too is $2^X$?
152382
Can an infinite set A be larger than an infinite set B but still have the same cardinality?
146421
How to prove a total order has a unique minimal element
91237
Every infinite set contains a countable subset
127200
Are there fields and ordered fields of every infinite cardinality?
140799
Prove that there exist uncountable family of subsets of $\mathbb{N}$ which is linearly (totally) ordered by relation of inclusion.
154578
Proving there is a sequence convergent to a limit point of a set without axiom of countable choice?
144181
Given an arbitrary set $X$, can one always find an element outside $X$?
52451
Ordered Triples and Set Theory
40937
Is the set of partial order relations over $ \mathbb{N}$ countable?
39880
Cardinality of Orderings of $\mathbb{R}$
117133
Is there an infinite countable $\sigma$-algebra on an uncountable set
128692
Example of an infinite group where every element except identity has order 2
82009
Prove that every totally ordered set has a well-ordered cofinal subset