New manuscript on Pfeiffer's thesis

martdowd at martdowd at
Thu Feb 17 17:17:06 EST 2022


I have continued my research on Pfeiffer's 1964 system of fundamental
sequences.  A preprint is available:
  Axioms for Fundamental Sequences

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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