[FOM] A New Ordinal Notation
Dmytro Taranovsky
dmytro at MIT.EDU
Mon Aug 8 13:33:45 EDT 2005
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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