New manuscript on Pfeiffer's thesis
martdowd at aol.com
martdowd at aol.com
Thu Feb 17 17:17:06 EST 2022
FOM:
I have continued my research on Pfeiffer's 1964 system of fundamental
sequences. A preprint is available:
Axioms for Fundamental Sequences
https://www.researchgate.net/publication/358676874
Abstract:
In 1964 H.\ Pfeiffer defined systems $\Sigma^n_p$ of fundamental sequences.
To show that $\Sigma^n_{p+1}$ exists it must be shown that $\Sigma^{n+1}_p$
has certain properties. This paper represents an effort to provide a new
treatment of this problem. Some axioms are defined, and an effort is made
to show that $\Sigma^{n+1}_1$ satisfies them.
Various properties of $\Sigma^{n+1}_1$ are shown,
and it is used to obtain a lower bound on the smallest repeat point.
I claimed in an earlier preprint that $\Sigma^n_2$ exists. I am no longer
certain that this is the case. I neglected to show that some designators
were maximal. If you don't know this then you don't know the
fundamental sequence. As I mentioned in an earlier post, I suspect
that Pfeiffer's thesis has this problem. In any case, it would be
of interest to continue the research of my write-up.
Martin Dowd
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