User blog comment:Scorcher007/Biggest ordinal's table/@comment-1605058-20180527075709/@comment-1605058-20180527154654

The hierarchy of strength is correct. The statement you quote basically says "if we replace \(V_\kappa\) with \(V_{\kappa+1}\) in the definition of [large cardinal], we get [the other large cardinal]". This doesn't have a direct translation to strengths of extensions of ZFC and MK. Basically, for any two large cardinals A and B with B stronger than A, ZFC+B is stronger than MK+A which is stronger than ZFC+A. Thus I don't think most of your claims about PTOs at the end are correct.

While at that, Z2+PD is equal in strength to (I believe) a conjunction of "there are n Woodin cardinals" for each n, ZFC+PD is equal to "there are infinitely many Woodin cardinals", ZF+AD is equal to "there are infinitely many Woodin cardinals with a measurable above them". Neither of those theories have the same PTO.

Also, I have no idea what you mean with "universe of inaccessible cardinal" and others. Could you clarify?