# User talk:Muhammad Bukhari Noor/Karauwan cardinal

## Spam

Hey, I just would like to nominate this article for deletion (I don't know how to actually do that, so I'm just leaving this comment). But this page was made by the notorious troll embi. (This is the DNA ordinal guy if that provides any context.) He's been spamming links to this page around on Discord, so I'd advise deleting the page and banning the IP that made it.

## Disclaimer

Shouldn't we do stuffs in a case by case basis? I mean, this article is clearly not trolling, and it actually contributes to mathematics. So why do you want to delete this? Unless Karauwan cardinals turned out to be ill-defined, but you can just point out the problems here so I will fix it Muhammad Bukhari Noor 21:28, 26 July 2021 I am adding pseudosignature. I think that with signatures this talk will be clearer. BartekChom (talk) 00:33, 30 July 2021 (PDT)

- Part of the issue is that the name "Karauwan" is the real name of a person you know, and it's not known if she gave permission for this to be public. C7X (talk) 12:40, 27 July 2021 (PDT)

- I probably see two little problems: (1) You wrote \(\forall A_0:\forall A_1:\cdots (A_0)\) instead of \(\forall V_0:\forall V_1:\cdots (A_0)\). (2) Is "Given ... then ..." a correct construction in English?
- Maybe you should move this page, for example to User:Muhammad Bukhari Noor/Karauwan cardinal. As far as I know, Prof. Joel David Hamkins is running this wiki and I do not know whether he repaired it for it to become a page about amateurs' ideas.
- On the merits, I am not a professional mathematician, in particular I know little about infinitary logic and I have no idea whether what you wrote makes sense. Actually I suspect that if it does, then professional mathematicians have already defined it.
- Hmm, \(L_{\kappa,\omega}\): less then \(\kappa\) terms for conjunction/alternative and finite number of quantifiers...
- You think that writing something like \(\kappa \text{ is a cardinal} \land \kappa>0 \land \kappa>1 \land \cdots \land \kappa>\aleph_0 \land \kappa>\aleph_1 \land \cdots \land \neg \exists \alpha<\kappa: (\alpha>0 \land \alpha>1 \land \cdots \land \alpha>\aleph_0 \land \alpha>\aleph_1 \land \cdots)\)
*[parenthesis after </math> seems to cause an error]*(i.e. writing that \(\kappa\) is the least cardinal greater than (listed) cardinals less than it) lets us define every cardinal (and the cardinality of symbols in the definition is no more than \(\kappa\)), yes? - If it is not an aleph fixed point, then the cardinality of symbols is less than \(\kappa\).
- For a singular cardinal we can use only the fundamental sequence (less symbols than \(\kappa\); for uncountable cofinality it is a sequence with uncountable length).
- For a successor cardinal the definition is trivial even in finitary logic and
- the least inaccessible cardinal can be defined in finitary logic too.

- You think that writing something like \(\kappa \text{ is a cardinal} \land \kappa>0 \land \kappa>1 \land \cdots \land \kappa>\aleph_0 \land \kappa>\aleph_1 \land \cdots \land \neg \exists \alpha<\kappa: (\alpha>0 \land \alpha>1 \land \cdots \land \alpha>\aleph_0 \land \alpha>\aleph_1 \land \cdots)\)
- Now I suspect that if it is consistent, then it is a real large cardinal (inaccessible and larger then the smallest ones). However, I assumed that we can use constants less then \(\kappa\) and you did not mention it (unless I overlooked it; besides, defining smaller cardinals seems to require less than \(\kappa\) symbols and maybe it does not increase the cardinality of the definition (on the other hand, I am not sure that the number of quantifiers will not become infinite — anyway, you can just write about using constants)).
- Next question: does Karauwan cardinal prove consistency of Mahlo cardinals? Measurable cardinals? It seems inaccessible and, by design, "indescribable" in some literal sense. Can this be the same as reflecting cardinals or one variant of indescribable cardinals? Probably you need help of a professional mathematician. Prof. Hamkins himself? Maybe p-bot knows enough and could help if he can be made to show good will. BartekChom (talk) 00:36, 30 July 2021 (PDT)