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Jun 18, 2011 at 13:04 comment added Todd Trimble Let's not get too hung up on words. You could call the sets of rank below the first inaccessible "small sets", those of rank below the second inaccessible "moderate sets", and those of arbitrary rank just "sets". Or, if you like you could rename them "sets", "classes", and "conglomerates". My point is that whatever you call them, "ZFC + two (strong) inaccessibles" more than suffices as a formal foundation for The Joy of Cats.
Jun 18, 2011 at 11:18 comment added porton But "Joy of Cats"'s "inaccessibles" are not sets, one of them is a proper class and the other is a conglomerate. Doesn't it affect anything?
Jun 18, 2011 at 0:27 history answered Todd Trimble CC BY-SA 3.0