Timeline for A question regarding $ZFC^{-}$
Current License: CC BY-SA 3.0
3 events
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| Dec 13, 2014 at 14:12 | comment | added | François G. Dorais | @ThomasBenjamin: Ah, you don't require $\sigma$ to be a theorem of $\mathrm{ZFC}$? Yes, compactness still applies: if $\mathrm{ZFC}^- \vdash \sigma\to\mathrm{Powerset}$ then this is provable in $\Sigma_n\mbox{-}\mathrm{KP}$ for some $n$. | |
| Dec 13, 2014 at 10:31 | comment | added | Thomas Benjamin | @FrancoisGDorais: Regarding the abstract extension of Ramsey's Theorem and its relation to $ZFC^{-}$--very interesting. Thanks. Since I only require that $ZFC^{-}$+$\sigma$$\vdash$Powerset and not full equivalence, is it correct to infer that by compactness, this implication is provable in $KP$ with infinity, $\Sigma_{n}$-separation and $\Sigma_{n}$-collection for some n? What I am really after is what $\sigma$ might be. | |
| Dec 13, 2014 at 3:59 | history | answered | François G. Dorais | CC BY-SA 3.0 |