[FOM] Possible non-existence of repeat points
martdowd at aol.com
martdowd at aol.com
Tue May 14 00:23:48 EDT 2019
FOM:
I have a new paper on lower bounds on the smallest repeat point.
The paper is titled
An Ordinal Larger Than the Bachmann-Howard Ordinal
It is temporarily available at
https://www.researchgate.net/publication/
333058459_An_Ordinal_Larger_Than_the_Bachmann-Howard_Ordinal
This gives a system of fundamental sequences of length $\psi_2^\Omega(0)$.
The closure ordinal is an ordinal larger than the Bachmann-Howard ordinal,
which is the closure ordinal of the system of fundamental sequences of length
$\psi_1^\Omega(0)$. Maximal indices for ordinals less than the closure
ordinal are shown to exist. The proof uses the method of built-up systems
of fundamental sequences, which originated with Bachmann and was further
developed by Schmidt. It is also used by Isles.
Using the maximal elements a system of fundamental sequences of length
$\psi^\Omega_{\psi^{\Omega^+}_2(0)}(0)$, or $\psi_{\psi_2(0)(0)$ for short,
is constructed. This is used to get the new bound.
Martin Dowd
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