FOM: The Church Thesis

Marcin Mostowski marcinmo at mail.uw.edu.pl
Thu Jan 25 07:06:04 EST 2001

Dear FOMers,
Recently, I have written the paper "Potential Infinity and
the Church Thesis" proposing essentially new "mathematical
proof of the Church Thesis. I hope the work can be interesting at least
for some FOMers. Unfortunately still I have no home page, then I cannot
send the persons interested there. However I can send "pdf" file
to everybody interested (it is easy to read and prit with Acrobat
reader). Also some other relevant papers (if necessary) can be send
in "pdf" format.
The abstract of the paper follows.

In this paper we consider the mathematical'' proof of Church
Thesis. The proof is based on very weak assumptions about {\em
intuitive computability} and {\em FM--representability theorem}
from \cite{MM-MLQ}. It develops and improves the argument from
\cite{MM-LMPS}. Our argument essentially depends on the
mathematical model of the world we are in. Finally we consider
another mathematical model of our world, in which the Church
Thesis appears to be very far from being true.

\bibitem{MM-MLQ}{\sc M. Mostowski},
{\em On representing concepts in finite models}, {\bf Mathematical
Logic Quaterly} 47(2001).

\bibitem{MM-LMPS}{\sc M. Mostowski},
{\em On representing semantics in finite models}, in {\bf
Procedings of Contributed Papers of the 19th LMPhS}, Kluwer