Timeline for Complexity of $Σ_n$ theory of $H(ω_2)$ under MM$^{++}$
Current License: CC BY-SA 4.0
7 events
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| Nov 25 at 0:33 | history | edited | Dmytro Taranovsky | CC BY-SA 4.0 |
updated with a possible answer from Woodin; added a generalization
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| Feb 27, 2021 at 13:31 | comment | added | matteo viale | I don't know how much you would find this related to your question but in arXiv2101.07573 it is shown that there is a recursive signature L (given by declaring atomic the Delta_0-formulae, the lightface definable universally Baire sets, the formula for NS) such that in signature L the theory of H(\omega_2) assuming P_max is model complete and there is a recursive set A of axioms given by Pi_2-sentence of LK such that in any model M of MM^++ the L-theory of H(omega_2) is given by the above recursive set A and the non recursive set given by the Pi_1-sentences of L holding in the model. | |
| Feb 25, 2021 at 16:44 | comment | added | Dmytro Taranovsky | @MonroeEskew Correct (see the last paragraph for how the answer may look like). | |
| Feb 25, 2021 at 16:40 | comment | added | Monroe Eskew | But what kind of answer do you seek? A description of how its degree relates to other well-known degrees? | |
| Feb 25, 2021 at 16:30 | comment | added | Dmytro Taranovsky | @MonroeEskew Complexity is the degree under many-one reducibility here. | |
| Feb 25, 2021 at 16:28 | comment | added | Monroe Eskew | What do you mean by, "What is the complexity?" | |
| Feb 25, 2021 at 16:12 | history | asked | Dmytro Taranovsky | CC BY-SA 4.0 |