Timeline for Forcing CH but not adding $\omega_1$-sequences
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 30, 2018 at 21:52 | history | edited | Noah Schweber | CC BY-SA 4.0 |
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| Aug 28, 2018 at 17:04 | history | edited | Noah Schweber | CC BY-SA 4.0 |
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| Aug 28, 2018 at 16:58 | history | edited | Noah Schweber | CC BY-SA 4.0 |
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| Aug 28, 2018 at 16:54 | comment | added | Noah Schweber | @JoelDavidHamkins To be fair, I think it's understating it to say that $M\models\neg$ CH is the "main case" since the other case is literally trivial. The point about extensions vs. forcing extensions is good, and I've added it to my answer. | |
| Aug 28, 2018 at 16:36 | comment | added | Joel David Hamkins | The OP didn't say that $M$ has $\neg$CH, although I suppose that would be the main case. What the argument shows is that CH is equivalent to the assertion that there is a forcing notion forcing CH without adding new $\omega_1$-sequences. Indeed, forcing has nothing to do with it. For any model $M$, there is an extension $N$ with CH and no new $\omega_1$-sequences if and only if CH is already true in M. | |
| Aug 28, 2018 at 2:37 | history | answered | Noah Schweber | CC BY-SA 4.0 |