User talk:C7XWiki

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Hi C7X
I'm on the googology wikia now under the same username. 

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 * Hi! C7XWiki (talk) 20:13, 23 September 2021 (UTC)

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OCFs
Would you want to collaborate on an ordinal collapsing function? I was thinking of creating thinning hierarchies consisting of iterated shrewdness diagonalized of degrees of unfoldability, which are in turn diagonalized by ethereal cardinals. If so, how would we collaborate? Should we use Google Docs? Binary198 (talk) 17:30, 21 February 2022 (UTC)


 * Sorry for not seeing this message for a while, I'd be happy to help! I can use Google Docs, although I'm sorry to say I know very little about unfoldable cardinals and elementary embeddings in general C7XWiki (talk) 10:21, 26 February 2022 (UTC)


 * Great! I don't 100% understand elementary embeddings myself (I have a vague idea). https://docs.google.com/document/d/1J2ThLBQ4PZe9L4MrOpeGhaFEGzovj_icluipIT49GeE/edit?usp=sharing Binary198 (talk) 16:13, 1 March 2022 (UTC)

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Well-ordering theorem
A while back you added a proof to the article Well-ordering theorem that the axiom of choice implies the well-ordering theorem. Near the end of the proof there's a notation using angle brackets. Is that a standard notation for ordered set? It might be good to add a brief explanation or a link explaining that. Will Orrick (talk) 18:30, 25 January 2024 (UTC)


 * I think I no longer have a copy of the book in the citation, but the notation seems to mean the well-ordering whose length is the supremum of the $$\alpha$$ where $$a_\alpha$$ is defined, and where the set placed at height $$\alpha$$ in the ordering is $$a_\alpha$$. The well-ordering itself as a set would be $$\{(a_\alpha,a_\beta)\mid a_\alpha,a_\beta\;\textrm{are}\;\textrm{defined}\land\alpha<\beta\}$$, although as this is an implementation detail I am not sure if this should be added to the article, in which case I am not sure what could be used to notate the ordering. Thanks for pointing this out! C7XWiki (talk) 22:06, 25 January 2024 (UTC)
 * Thanks for the reply. That clears it up for me. My feeling is that it would be better to conclude the proof without introducing an unfamiliar notation. I don't know if the following is a too long-winded replacement for the final sentence: "Then the order $$<$$ on $$A$$ defined by $$a_\alpha < a_\beta$$ if and only if $$\alpha<\beta$$ (in the usual well-order of the ordinals) is a well-order of order type $$\sup\{\alpha \mid a_\alpha\text{ is defined}\}$$." Will Orrick (talk) 17:16, 26 January 2024 (UTC)


 * That form sounds fine, I will add it into the article. Thanks! C7XWiki (talk) 06:33, 28 January 2024 (UTC)