[FOM] Possible non-existence of repeat points
martdowd at aol.com
martdowd at aol.com
Tue Oct 17 13:07:46 EDT 2017
FOM:
Following up on
http://www.cs.nyu.edu/pipermail/fom/2017-May/020479.html
http://www.cs.nyu.edu/pipermail/fom/2017-May/020506.html
I have just submitted
THE SMALLEST REPEAT POINT IN MITCHELL'S MODEL
It's temporarily available at www.hyperonsoft.com/lblu.pdf
Abstract:
It is shown that the smallest ordinal $\theta_T$ such that there is no
T-separating set at $\theta_T$ is at least an ordinal which is the large
Veblen ordinal for the infinitary Veblen function starting at the
critical point enumerator $C$. This holds for any coherent sequence
satisfying $o({\cal U}(\kappa)(\beta))=\beta$. A function $W$ is
defined in Mitchell's model $L[{\cal U}]$, and $\theta_T$ is shown to be
closed under $W$. This does not yield any improvement to the $C$ bound.
It is shown using $C$ and $W$ that in $L[{\cal U}]$, if $\theta<\theta_T$
then $\Pow(\kappa)\not\subseteq L_\theta[{\cal U}]$.
The earlier posts have links to earlier manuscripts. These have bugs,
which are fixed in the new manuscript.
The question arises of upper bounds on $\theta$ such that in
$L{\cal U}]$, $\Pow(\kappa)\subseteq L_\theta[{cal U}]$.
This has been posted to mathoverflow as question no. 283644.
Regards,
Martin Dowd
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