02/23/2008, 03:33 AM
Hmm, apparently, I'm not the first one to discover the correlation between higher-order arithmetic operations and the recursive transfinite ordinals:
http://mathforum.org/kb/thread.jspa?messageID=371175
According to this page, the Feferman-Schütte ordinal \( \Gamma_0 \) is the supremum of all ordinals (finitely) describable using recursive operations. Yet it is still recursive (and therefore computable), so I wonder if there may be a way to reach it. Obviously, some other method than merely building on previous operations will be needed.
http://mathforum.org/kb/thread.jspa?messageID=371175
According to this page, the Feferman-Schütte ordinal \( \Gamma_0 \) is the supremum of all ordinals (finitely) describable using recursive operations. Yet it is still recursive (and therefore computable), so I wonder if there may be a way to reach it. Obviously, some other method than merely building on previous operations will be needed.
