Timeline for On the Actual Potential of Virtual Large Cardinals
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jul 24, 2018 at 22:34 | comment | added | Morteza Azad | Very kind of you, Joel! Thanks again for contributing to this post! :-) | |
| Jul 24, 2018 at 22:29 | comment | added | Joel David Hamkins | I wrote to Vika, who we may hope may post an answer there. | |
| Jul 24, 2018 at 21:54 | vote | accept | Morteza Azad | ||
| Jul 24, 2018 at 21:47 | comment | added | Morteza Azad | OK! Done! Here is the new question: What are examples of non-equivalent virtualizations of a large cardinal? | |
| Jul 24, 2018 at 20:48 | comment | added | Joel David Hamkins | I'd suggest a separate and more focused question, asking for instances where the virtualization process depends on the particular equivalent form of a large cardinal. I think one can ask it without writing much, which will make it easier for people to understand. | |
| Jul 24, 2018 at 20:41 | comment | added | Morteza Azad | This is a really interesting point! I actually wanted to add it as a third question to this post but I hesitated as I thought it might be trivial. So let me update the original post now. By the way, it would be great if Vika adds more details concerning this very issue and of course about her criteria for choosing the right characterization of a large cardinal to virtualize. | |
| Jul 24, 2018 at 20:33 | comment | added | Joel David Hamkins | No, it isn't true. In fact, sometimes it is a bit finicky to get the right notion to "virtualize". For example, in the remarkable case, they virtualized the Magidor version of supercompactness, and if I recall correctly, doing a naive virtualization with other characterizations of supercompactness were not the same. Perhaps we can convince Victoria to post an answer about this. | |
| Jul 24, 2018 at 20:27 | comment | added | Morteza Azad | (+1) Interesting use of games! Thank you, Joel! Another question if I may: As mentioned in the OP, based on a result of Gitman and Schindler, it turns out that different large cardinals may have equivalent virtualizations. For instance, there are characterizations of supercompacts and strong cardinals whose virtualization are equivalent to remarkables. So virtualization doesn't preserve consistency strength order strictly. Conversely, I wonder whether it is trivial that the virtualization of all equivalent characterizations of the same large cardinal are equivalent or I am missing something. | |
| Jul 24, 2018 at 19:42 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
added 529 characters in body
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| Jul 24, 2018 at 19:36 | history | answered | Joel David Hamkins | CC BY-SA 4.0 |