Timeline for A new cardinality living in every forcing extension?
Current License: CC BY-SA 4.0
22 events
| when toggle format | what | by | license | comment | |
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| Feb 2, 2022 at 4:11 | vote | accept | Noah Schweber | ||
| Jun 29, 2021 at 5:40 | answer | added | Harry West | timeline score: 1 | |
| S Jul 30, 2020 at 22:06 | history | bounty ended | CommunityBot | ||
| S Jul 30, 2020 at 22:06 | history | notice removed | CommunityBot | ||
| Jul 23, 2020 at 14:26 | comment | added | Noah Schweber | @AsafKaragila That's my suspicion too, but I don't see how to prove it. | |
| Jul 23, 2020 at 14:25 | comment | added | Asaf Karagila♦ | Ah yes. I still don't see how you can even get this thing to exist. If you added a new cardinal number, I don't see how it could possibly satisfy this key requirement without also being equipotent with a ground model object. Genericity is really strong. | |
| Jul 23, 2020 at 13:01 | comment | added | Noah Schweber | @AsafKaragila Because it missed the key requirement $\Vdash_{\mathbb{P}^2}\nu[G_0]\equiv\nu[G_1]$. | |
| Jul 23, 2020 at 6:54 | comment | added | Asaf Karagila♦ | Remind me again, what was the issue with my now-deleted answer, where I gave an example of a model of $\sf ZF$ in which there is a forcing and a name $\nu$ such that $\nu[G]$ is guaranteed to have a different cardinality than all ground model objects? | |
| Jul 22, 2020 at 21:54 | history | edited | Noah Schweber | CC BY-SA 4.0 |
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| Jul 22, 2020 at 21:45 | history | edited | Noah Schweber | CC BY-SA 4.0 |
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| S Jul 22, 2020 at 20:55 | history | bounty started | Noah Schweber | ||
| S Jul 22, 2020 at 20:55 | history | notice added | Noah Schweber | Draw attention | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 15, 2015 at 19:32 | comment | added | Asaf Karagila♦ | @François: But do you have to force back the axiom of choice? No, you don't have to force it back. | |
| Jan 7, 2015 at 3:37 | history | edited | Noah Schweber | CC BY-SA 3.0 |
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| Jan 7, 2015 at 2:58 | comment | added | François G. Dorais | Yeah, that's the "half-baked" part. The thing is that with SVC you can force AC for reasons totally unrelated to the "generic cardinal" and that seems like an issue. I haven't thought this through much so I'm not even convincing myself with this idea but it's not outright ridiculous... | |
| Jan 7, 2015 at 2:41 | comment | added | Noah Schweber | It's always possible for the generic cardinality to be made "uninteresting": just collapse it to $\omega$. (This is what I'm getting at in the paragraph mentioning bad behavior of equinumerosity.) I'm not sure we can conclude even that no model of SVC admits a "nonexistent generic cardinality," but maybe I'm missing something. | |
| Jan 7, 2015 at 2:40 | comment | added | François G. Dorais | This is just a "half-baked" thought: if $V$ satisfies SVC then one could force AC and that would make the generic cardinality "uninteresting". So, I guess, if there is such a thing then AC must fail "really badly" in $V$. | |
| Jan 7, 2015 at 2:39 | history | edited | Noah Schweber | CC BY-SA 3.0 |
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| Jan 6, 2015 at 23:17 | history | edited | Asaf Karagila♦ | CC BY-SA 3.0 |
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| Jan 6, 2015 at 21:42 | history | edited | Noah Schweber | CC BY-SA 3.0 |
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| Jan 6, 2015 at 21:35 | history | asked | Noah Schweber | CC BY-SA 3.0 |