[FOM] A New Ordinal Notation

[Lew Gordeew]

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
> 
> _______________________________________________
> FOM mailing list
> FOM at cs.nyu.edu
> http://www.cs.nyu.edu/mailman/listinfo/fom
> 

-- 
GMX DSL = Maximale Leistung zum minimalen Preis!
2000 MB nur 2,99, Flatrate ab 4,99 Euro/Monat: http://www.gmx.net/de/go/dsl

-- 
GMX DSL = Maximale Leistung zum minimalen Preis!
2000 MB nur 2,99, Flatrate ab 4,99 Euro/Monat: http://www.gmx.net/de/go/dsl

-- 
5 GB Mailbox, 50 FreeSMS http://www.gmx.net/de/go/promail
+++ GMX - die erste Adresse für Mail, Message, More +++