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Topic: Van Neumann Hierarchy
Replies: 13   Last Post: Apr 28, 2014 10:45 AM

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David C. Ullrich

Posts: 3,555
Registered: 12/13/04
Re: Van Neumann Hierarchy
Posted: Apr 26, 2014 2:18 PM
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On Fri, 25 Apr 2014 20:13:43 -0700, William Elliot <>

>The Van Neumann hierarchy is defined with transfinite induction as
> V_eta = \/{ P(V_xi) | xi < eta }.

Huh> That reminds me of the Von Neumann hierarchy...

>Within ZF, using regularity and replacement, how does one show
>that for every set A, there's some ordinal eta, with A in V_eta.
>It would suffice to show for every transitive set A,
>there's some ordinal eta, with A in V_eta.
>With that, since every set is a subset of it's transitive

You really really really need to stop criticizing others' English.
Or learn a little English yourself. It's "its", not "it's".

>closure, every set would be inside the Van Neumann hierarchy.

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