Timeline for How many reals can we construct by iteratively writing down truth tables for ZFC?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 8, 2021 at 22:34 | vote | accept | zeb | ||
| Feb 8, 2021 at 7:12 | answer | added | Gabe Goldberg | timeline score: 5 | |
| Feb 6, 2021 at 18:00 | comment | added | Gabe Goldberg | I have to think a bit more about the ordertype, which is interesting. Seems the same as the question of whether the canonical wellorder of OD sets restricts to a wellorder of the OD reals in ordertype $\mathfrak{c}^\text{HOD}$. That might be independent. | |
| Feb 6, 2021 at 17:53 | comment | added | zeb | You haven't completely misunderstood - I'd be happy to accept that as an answer! | |
| Feb 6, 2021 at 17:22 | comment | added | Gabe Goldberg | Every real definable in $V_\alpha$ will be computable from $T(\alpha)$ since $\alpha$ is coded into $T\restriction \alpha$. So every ordinal definable real is computable from a $T(\alpha)$. Also every real you enumerate will be ordinal definable: in MK, there is a proper class of $\alpha$ with $V_\alpha\prec V$. So the set of fresh ordinals has cardinality the continuum in $\text{HOD}$. Not sure about the order type. I'll post an answer later if I haven't completely misunderstood the question. | |
| Feb 6, 2021 at 14:13 | history | edited | zeb | CC BY-SA 4.0 |
realized that one of the questions was trivial
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| Feb 6, 2021 at 5:28 | comment | added | Noah Schweber | @AndreasBlass Yes, I meant MK. Not my finest moment. | |
| Feb 6, 2021 at 5:08 | comment | added | Andreas Blass | @NoahSchweber It seems to me that the class theory you want should be MK rather than NBG, so that truth in $V$ becomes definable. | |
| Feb 6, 2021 at 3:20 | comment | added | Noah Schweber | Note that we can remove the philosophical flavor here by just working inside an appropriate class theory, e.g. $\mathsf{NBG}$ (at a glance I think that should be enough for what you want here). In particular, in this ambient class theory we can legitimately talk about $T$ and so forth without difficulty. | |
| Feb 6, 2021 at 3:14 | history | asked | zeb | CC BY-SA 4.0 |