Timeline for When do infinitary compactness numbers exist?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 2, 2022 at 18:16 | comment | added | Noah Schweber | Nope, I'm just bad at math once it gets past 8pm or so. :P Thanks! | |
| Feb 2, 2022 at 18:02 | comment | added | Gabe Goldberg | The argument in the second-to-last paragraph above seems to yield that if $\delta$ is the compactness number for $\mathcal L_{\kappa,\omega}$, then every $\delta$-complete filter extends to a $\kappa$-complete ultrafilter; i.e., $\delta$ is $\kappa$-compact. Conversely, if $\delta$ is $\kappa$-compact, it is greater than or equal to the compactness number for $\mathcal L_{\kappa,\kappa}$, which in turn is at least the compactness number for $\mathcal L_{\kappa,\omega}$. Am I missing something? | |
| Feb 2, 2022 at 4:15 | comment | added | Noah Schweber | A couple years later, what happens with $\mathcal{L}_{\kappa,\omega}$ instead? (The inability to characterize well-foundedness seems like an issue for this argument, but I might be having a stupid moment.) | |
| Oct 25, 2020 at 22:08 | history | edited | Gabe Goldberg | CC BY-SA 4.0 |
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| Oct 25, 2020 at 21:22 | comment | added | Gabe Goldberg | Yes you're right, I'll add the details. | |
| Oct 25, 2020 at 21:21 | comment | added | Noah Schweber | Sorry, I'm having a silly moment; I don't immediately see the theory you describe in the second part of the last paragraph (getting from compactness numbers to large cardinals). At the very least it seems that we should have names for all subsets of $P_\delta(X)$, not just of $X$. Can you add some details? | |
| Oct 24, 2020 at 2:45 | vote | accept | Noah Schweber | ||
| Oct 24, 2020 at 0:51 | history | edited | Gabe Goldberg | CC BY-SA 4.0 |
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| Oct 23, 2020 at 23:55 | history | edited | Gabe Goldberg | CC BY-SA 4.0 |
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| Oct 23, 2020 at 23:04 | history | answered | Gabe Goldberg | CC BY-SA 4.0 |