Given an infinite poset, show that it contains either a infinite chain or an infinite totally unordered set.
6478
Prove that for any infinite poset there is an infinite subset which is either linearly ordered or antichain.
12436
The cardinality of the set of all finite subsets of an infinite set
86926
Why isn't this a well ordering of $\{A\subseteq\mathbb N\mid A\text{ is infinite}\}$?
48278
Inequality about infinite cardinals
113668
Uncountable chain of subsets of $\mathbb N$
99478
countably infinite union of countably infinite sets is countable
33894
How many chains are there in a finite power set?
106455
intersection of infinite collection of finite sets?
120273
Showing that a collection of sets is a $\sigma$-algebra: either set or complement is countable
38242
Explicit bijection between the successor of $\alpha$ and $\alpha$ (infinite ordinal).
102202
The smallest infinity and the axiom of choice
36281
A set is infinite iff it is equivalent to a proper subset of itself
14972
Cardinality of Vitali sets: countably or uncountably infinite?
123090
How to show that disjoint closed sets have disjoint open supersets?
118595
Proving that a set is countable by finding a bijection
117561
A set is infinite iff there is a one-to-one correspondent with one of its proper subsets?
144787
Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$