Talk:Huge cardinal

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[edit] Question

In the formula

κ is almost huge iff there is j : V → M with critical point κ and <j(κ)M ⊂ M.

I am having trouble understanding the notation <j(κ)M ⊂ M.

And in the formula

κ is n-huge iff there is j : V → M with critical point κ and j^n (κ)M ⊂ M.

should

j^n (κ)M ⊂ M

be

jn (κ)M ⊂ M ?

Is this standard notation? Oleg Alexandrov 00:00, 28 May 2005 (UTC)

  • j^n refers to the nth iterate of the function j. It should be superscripted again, but I don't know if that can be done in HTML. The <j(kappa) bit means that M need only be closed under sequences with length less than kappa, rather than sequences of length kappa.

Ben Standeven 04:49, 29 May 2005 (UTC)

Thanks! Oleg Alexandrov 14:56, 29 May 2005 (UTC)

[edit] Totally huge cardinals

Is there such a thing as a totally huge cardinal, meaning one that is nhuge for all n? (I mean, are these considered, and under that name?) The analogy here is with the totally ineffable cardinals. -- Toby Bartels 08:31, 13 December 2005 (UTC)

I think that "totally huge" would be a Reinhardt cardinal which is inconsistent with the axiom of choice. JRSpriggs 09:44, 3 May 2006 (UTC)

[edit] Critical point

What is a critical point, in this context? The current link seems inappropriate. It surely has nothing to do with any kind of derivative. The Infidel 15:04, 22 January 2006 (UTC)

Critical point (set theory) has been fixed now (I hope). Please look at it again. JRSpriggs 06:32, 2 May 2006 (UTC)
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