Timeline for Can the Turing degrees be linearly ordered?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 29, 2018 at 14:31 | vote | accept | Noah Schweber | ||
| Jan 25, 2018 at 14:04 | comment | added | Andrés E. Caicedo | @Noah As Paul mentioned, the key is that you can embed $\mathbb R/E_0$ into $\mathcal D $. (In my paper with Ketchersid, we explain that in natural determinacy models, for instance, a set is not linearly orderable if and only if there is such an injection.) | |
| Jan 25, 2018 at 13:39 | answer | added | Paul Larson | timeline score: 13 | |
| Jan 25, 2018 at 12:01 | history | edited | Noah Schweber | CC BY-SA 3.0 |
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| Jan 25, 2018 at 12:01 | comment | added | Noah Schweber | @GerhardPaseman I'm not sure what you mean. | |
| Jan 25, 2018 at 12:01 | comment | added | Noah Schweber | @StevenStadnicki In ZF there is of course a surjection from $2^\omega$ onto $\mathcal{D}$, but I don't know about an injection the other way - I don't think that exists without choice. | |
| Jan 25, 2018 at 6:17 | comment | added | Steven Stadnicki | I thought it was well-established that there are exactly $2^\omega$ Turing degrees; does that argument use Choice? | |
| Jan 25, 2018 at 5:36 | comment | added | Gerhard Paseman | Can you try mimicking the ordering of the surreal numbers? Or does that require too much choice? Gerhard "Seems Bizarre To A Degree" Paseman, 2018.01.24. | |
| Jan 25, 2018 at 4:52 | history | edited | Noah Schweber | CC BY-SA 3.0 |
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| Jan 25, 2018 at 4:47 | history | asked | Noah Schweber | CC BY-SA 3.0 |