[FOM] A New Ordinal Notation
Lew Gordeew
legor at gmx.de
Wed Aug 10 02:04:24 EDT 2005
Would you please explicitly expose primitive recursive definitions of your
basic relations < and = in the system of notations built up from 0 and
C(-,-,-) ?
Regards,
LG
> I have discovered an ordinal notation system for rudimentary set theory
> + "for every ordinal alpha, there is recursively alpha-inaccessible
> ordinal," which may be simpler and more natural than the standard
> notation.
>
> I have also discovered what may be an ordinal notation system for full
> second order arithmetic; however, I do not have a proof of its
> correctness. A key idea is assignment of reflection degrees to
> ordinals. An ordinal has degree alpha+1 iff it has degree alpha and is
> below a certain ordinal (that is dependent on alpha) or is a limit of
> ordinals of degree alpha. An ordinal has degree gamma where gamma is
> limit iff it has every degree less than gamma. The notation is built
> >from constants and a function C such that C(alpha, beta) is the least
> ordinal above beta that has degree alpha.
>
> Details are in my paper
> http://web.mit.edu/dmytro/www/other/OrdinalNotation.htm
>
> Dmytro Taranovsky
>
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