Timeline for Is there an abstract logic that defines the mantle?
Current License: CC BY-SA 4.0
4 events
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| Jul 28, 2020 at 0:06 | comment | added | Gabe Goldberg | In that case, it seems like the $C(\mathcal L)$ must be contained in $\text{HOD}_{\text{Ord}^\kappa,S}$ for some set $S$ (corresponding to the set of sentences) and some cardinal $\kappa$ (corresponding to the number of free variables allowed in a single sentence sentence). I bet you can get a model where the mantle is not contained in $\text{HOD}_{\text{Ord}^\kappa,S}$ for any $\kappa$ and $S$. It may be interesting to look instead at logics that have a Lowenheim number. | |
| Jul 27, 2020 at 23:46 | comment | added | Noah Schweber | Of course, this is a proper-class-sized logic - it would be quite reasonable to ask for a set-sized logic, that is, one whose class of $\Sigma$-formulas is a set for each language $\Sigma$. And then I see no similar trick. | |
| S Jul 27, 2020 at 20:30 | history | answered | Hanul Jeon | CC BY-SA 4.0 | |
| S Jul 27, 2020 at 20:30 | history | made wiki | Post Made Community Wiki by Hanul Jeon |