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

 Messages: [ Previous | Next ]
 David C. Ullrich Posts: 3,555 Registered: 12/13/04
Re: Van Neumann Hierarchy
Posted: Apr 26, 2014 2:18 PM

On Fri, 25 Apr 2014 20:13:43 -0700, William Elliot <marsh@panix.com>
wrote:

>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.

Date Subject Author
4/25/14 William Elliot
4/26/14 David Hartley
4/27/14 William Elliot
4/27/14 David Hartley
4/27/14 William Elliot
4/28/14 William Elliot
4/26/14 David C. Ullrich
4/26/14 Sandy
4/26/14 William Elliot
4/27/14 Sandy
4/27/14 William Elliot
4/27/14 David C. Ullrich
4/27/14 Sandy
4/28/14 David C. Ullrich