TITLE: A question about large cardinal axioms.
QUESTION [5 upvotes]: Can all the large cardinal axioms not presently known to be
inconsistent with ZFC be arranged in a strict linear order based
on the following criterion. Let A(1) and A(2) be any distinct pair
of these axioms and let both be adjoined to ZFC. We will say that
$A(1)\lt A(2)$ if and only if the smallest cardinal number satisfying A(1)
is smaller than the smallest cardinal number satisfying A(2). Should
such a strict linear ordering of these axioms be possible, which of
them ranks the largest?

REPLY [6 votes]: Just to give a short, explicit example of the local-versus-global issue that Andres mentioned, consider supercompactness (global) and hugeness (local).  In terms of consistency strength, hugeness is far stronger than supercompactness.  Yet, if there exist both a supercompact cardinal and a huge cardinal, then the first supercompact cardinal is larger than the first huge cardinal.