Timeline for Is the collection of isomorphism classes of groups a proper class?
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| Jun 22, 2022 at 8:13 | history | edited | CommunityBot |
replaced http://math.uga.edu/~pete with http://alpha.math.uga.edu/~pete
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| Jan 25, 2010 at 13:24 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
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| Jan 25, 2010 at 13:23 | comment | added | Joel David Hamkins | About your AC remark and cardinal arithmetic: If ZF, you can prove that kappa^2=kappa for any infinite (well-ordered) cardinality, so yes, kappa\times\aleph_0 = kappa for such kappa. If you mean "cardinal" in the not-AC sense, however, then if kappa is infinite but Dedekind finite, it cannot have \kappa\times\aleph_0 = \kappa, since this implies a countably infinite subset. But to get the proper class of models, as you suggest, one needs to use only the well-ordered cardinals. | |
| Jan 25, 2010 at 13:14 | history | answered | Pete L. Clark | CC BY-SA 2.5 |