Timeline for V=HOD & The Height of the Large Cardinal Tree
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 14, 2013 at 13:30 | vote | accept | CommunityBot | ||
| Dec 14, 2013 at 2:52 | comment | added | Andrés E. Caicedo | (I really like the lottery, by the way, it really simplifies many arguments.) | |
| Dec 14, 2013 at 2:47 | comment | added | Andrés E. Caicedo | Let me further add that we expect the pattern to persist, to the point that the canonical inner models for large cardinals are explicitly built as subclasses of $\mathsf{HOD}$. There is also another comment that may be useful: There are "global" large cardinals (such as supercompactness) but we have local versions for all (such as: There is an inaccessible $\kappa$ such that in $V_\kappa$ there is a proper class of supercompact cardinals). For any such (local) cardinal, showing its consistency with $V=\mathsf{HOD}$ is straightforward via the GCH coding starting at a cardinal sufficiently high. | |
| Dec 14, 2013 at 0:14 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Dec 13, 2013 at 23:56 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
added 145 characters in body
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| Dec 13, 2013 at 23:50 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |