User blog comment:DontDrinkH20/Some Explanations of Certain Large Cardinals/@comment-11227630-20181017041904/@comment-11227630-20181017052722

That sounds bad.

What about only choosing some cardinals, and order them, where "property A is stronger than B" means
 * An A-cardinal is a B-cardinal, and the smallest B-cardinal is not an A-cardinal.

And make the "cardinal implication chain" cover as many cardinal properties as possible?