Timeline for What is the modal logic of outer multiverse?
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Jul 19, 2018 at 9:40 | vote | accept | Morteza Azad | ||
| Jul 19, 2018 at 0:11 | comment | added | Joel David Hamkins | But to address your final comment: no, there isn't in general a way to deduce the downward logic from the upward logic, since there are Kripke models with the same upward logics, but different downward logics. In the case of forcing, for example, Benedikt Löwe and I considered this in our paper, Up and down in the generic multiverse. | |
| Jul 18, 2018 at 23:59 | comment | added | Joel David Hamkins | @Gro-Tsen Your comment is related to the issue of the Solovay modalities for rank potentialism, namely, "true in all $V_\kappa$," interpreted in a downward sense. Solovay similarly verifies GL logic, as you noticed. Linnebo and I point out that this concept of accessbility is not potentialist, and we discuss this at length in our paper linked in my answer. | |
| Jul 18, 2018 at 23:50 | comment | added | Gro-Tsen | How about asking the question for inner models? (I feel it is more natural to jump "into" worlds than "out of" them.) Do you already know the answer for that? I imagine it should be very similar to the logic of provability (cf. Boolos's book with that title), e.g., I think Löb's axiom holds. Now isn't there a pure modal logic way to reverse the accessibility arrows? | |
| Jul 18, 2018 at 23:05 | answer | added | Joel David Hamkins | timeline score: 23 | |
| Jul 18, 2018 at 23:00 | review | Close votes | |||
| Jul 19, 2018 at 14:13 | |||||
| Jul 18, 2018 at 20:12 | history | edited | Morteza Azad |
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| Jul 18, 2018 at 19:50 | history | asked | Morteza Azad | CC BY-SA 4.0 |