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Full Idea
Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable).
Gist of Idea
There are at least eleven types of large cardinal, of increasing logical strength
Source
Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4)
Book Ref
-: 'Philosophia Mathematica' [-], p.10
A Reaction
[I don't understand how cardinals can have 'logical strength', but I pass it on anyway]