Timeline for Is the collection of isomorphism classes of groups a proper class?
Current License: CC BY-SA 2.5
5 events
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| Jan 25, 2010 at 13:28 | comment | added | Pete L. Clark | @JDH: yes, that's pretty much the argument of the first link I provided below (not including the parenthetical part of your remark). | |
| Jan 25, 2010 at 13:17 | comment | added | Joel David Hamkins | If the cardinals were a set, then their supremum would be a largest cardinal. But there is no largest cardinal, since (in ZFC) Cantor proved kappa < 2^kappa. (In ZF, one can similarly show kappa+ exists, and kappa < kappa+, so AC is not needed.) | |
| Jan 25, 2010 at 11:34 | comment | added | S. Carnahan♦ | I should clarify: I'm pretty sure set theorists would say that the claim "cardinals form a proper class" is a standard result, e.g., in ZFC. I happen to think that a careful proof of this is trickier than any of the listed group constructions, but that may say more about my background than anything else. | |
| Jan 25, 2010 at 9:24 | comment | added | Hans-Peter Stricker | I agree with you, I immediately stumbled over this after having read Andrew's answer. | |
| Jan 25, 2010 at 9:20 | history | answered | S. Carnahan♦ | CC BY-SA 2.5 |