Show that given a partial order there exists a total order
76521
Every partial order can be extended to a linear ordering
146062
A "Cantor-Schroder-Bernstein" theorem for partially-ordered-sets
31091
Prove that there exist a branch
134049
Showing an inequality is valid
55328
Let $σ$ be the relation on $R×R$ in which $(a,b) σ (x,y)$ if and only if $a ≤ x$ and $b ≤ y$. Prove that $σ$ is a partial order relation.
6478
Prove that for any infinite poset there is an infinite subset which is either linearly ordered or antichain.
148774
show elements of order 15 in $S_8$ satisfy a relation
93655
How to prove the lack of implicit order in a database?
2396
Order-preserving injections of ordinals into $[0,1]$
22482
How can an ordered pair be expressed as a set?
126569
Can we find a well ordering on an infinite set with no largest element?
146421
How to prove a total order has a unique minimal element
94947
How to turn a system of first order into a second order
131946
Order of an Element Under a Homomorphism
141529
Proving existence of a minimum
96025
Showing there is only one isomorphism between well ordered sets using transfinite induction
44224
Understanding the order() function