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    $\begingroup$ Just a note: of the three relations you define, one is not like the others. Your “>” and “=” are ordinary statements of set theory, while your “~” is a meta-statement about provability (in ZFC, I assume). The cognoscenti are used to this, but it’s helpful to be explicit about it: conversations can get very muddled when some participants miss this sort of issue. $\endgroup$
    – Peter LeFanu Lumsdaine
    Commented Sep 24, 2015 at 7:54
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    $\begingroup$ The use of $\sim$ for undecidability seems particularly strange. How about $\bot$ instead? $\endgroup$
    – Asaf Karagila ♦
    Commented Sep 24, 2015 at 8:22
  • $\begingroup$ Related question: mathoverflow.net/questions/218414/… $\endgroup$
    – Timothy Chow
    Commented Sep 24, 2015 at 20:33
  • $\begingroup$ I said that this question is a duplicate of the question mentioned by @TimothyChow but now I see that the latter question is specifically whether the size hierarchy is the same as the consistency strength hierarchy. $\endgroup$
    – Arvid Samuelsson
    Commented Apr 2, 2022 at 10:21