Timeline for How strong is limitation of size + generalized continuum hypothesis?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 12, 2017 at 1:56 | comment | added | Zetapology | Just so you know, the Axiom of Limitation of Size implies, with only a little axiomatization (specifically $\mathrm{Ord}$ is well-ordered by $\in$ and every subclass of a well-orderable class is well-orderable), that every class is well-orderable. This is a strengthening of AC, which was already a strong axiom to begin with. ZF + Axiom of Limitation of Size is strong enough to prove ZFC. | |
| Jun 29, 2014 at 13:41 | answer | added | Thomas Klimpel | timeline score: 1 | |
| Jun 23, 2014 at 7:01 | comment | added | Sam Roberts | It is straightforward to show that limitation of size is equivalent to (second-order) Replacement and Global Choice over bounded Z + predicative second-order comprehension. Let T = bounded Z + LoS + predicative SO-comp. Then it follows that T + GCH is equivalent to NBG + Global Choice + GCH. Assuming NBG doesn't include Global Choice already, I take it that NBG + GCH won't imply T + GCH. However, since NBG + Global Choice is conservative over NBG + Choice and since GCH implies Choice, T + GCH is conservative over NBG + GCH. | |
| Jun 23, 2014 at 0:15 | comment | added | Thomas Klimpel | This question is based on a wrong assumption about the reason for the strength of pocket set theory (not limitation of size, but an impredicative class comprehension axiom leads to the strength). If this wrong assumption is fixed, all that remains of the question is basically which axioms can be omitted from NBG, if "limitation of size" (and maybe also GCH) is added as an axiom. The answer to that question can probably be found quite easily, potentially even on wikipedia... | |
| Jun 22, 2014 at 23:02 | answer | added | Asaf Karagila♦ | timeline score: 6 | |
| Jun 22, 2014 at 22:47 | history | asked | Thomas Klimpel | CC BY-SA 3.0 |