Re: L & R
From: H. Enderton (hbe_at_sonia.math.ucla.edu)
Date: 08/26/04
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Date: Thu, 26 Aug 2004 17:19:42 +0000 (UTC)
First Mike Oliver <mike_lists@verizon.net> wrote:
>>All the reals that ever show up, show up at some countable (in L) stage.
>>So every real in L is an element of L_{omega_1^L}. Then R^L itself
>>is a definable subset of that stage, so it shows up at the next
>>stage, L_{omega_1^L+1}.
And then Tim Chow wrote:
>Is this result sharp? That is, is it provable in ZF that R^L *doesn't*
>appear any sooner?
It can't appear sooner. L_alpha, for countable alpha, is countable.
Put yourself inside L. R is uncountable.
--Herb Enderton
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