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Mar 9, 2011 at 13:37 comment added Peter LeFanu Lumsdaine @Carl Mummert: that’s true — but similarly, Euclid could have said “there are arbitrarily large prime numbers”. In each case, there’s a slight difference in connotations; I can see why Larson might have considered both options and chosen what he did. [Oblig. note: IANAHOM; I do not know how Euclid actually worded that theorem.]
Mar 9, 2011 at 8:46 vote accept Hans-Peter Stricker
Mar 9, 2011 at 4:30 comment added Jason +1, I was just typing that as an answer and was going to reference Larson as well. Also do a Google search for: "proper class many" cardinals.
Mar 9, 2011 at 4:28 comment added Carl Mummert In that quote, the author could just say "arbitrarily large Woodin cardinals". Every set of cardinals is bounded, so any unbounded class of cardinals is a proper class.
Mar 9, 2011 at 4:23 history answered Peter LeFanu Lumsdaine CC BY-SA 2.5