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 Tetration and higher-order operations on transfinite ordinals quickfur Junior Fellow Posts: 22 Threads: 1 Joined: Feb 2008 02/23/2008, 05:46 PM You do realize that that's just the Ackermann function applied to omega, right? w[w]w = A(w,w), which corresponds with phi_2(0). That's definitely computable, although not primitive recursive. (Primitive recursive functions correspond with the operations of finite order.) But, as I've said above, the Ackermann function is but a mere scratch at the top 0.01% of the tip of the iceberg. As it stands, I've only barely made it 1% of the way down from the top of the tip of the iceberg---I still have no idea how to computationally get to phi_phi_1(0). And that's but one puny step out of infinitely-many needed to reach the Feferman-Schütte ordinal. (And this is disregarding the fact that every subsequent step is immensely larger than all previous steps combined.) « Next Oldest | Next Newest »

 Messages In This Thread Tetration and higher-order operations on transfinite ordinals - by quickfur - 02/21/2008, 08:16 PM RE: Tetration and higher-order operations on transfinite ordinals - by quickfur - 02/23/2008, 03:33 AM RE: Tetration and higher-order operations on transfinite ordinals - by GFR - 02/23/2008, 09:47 AM RE: Tetration and higher-order operations on transfinite ordinals - by quickfur - 02/23/2008, 05:46 PM RE: Tetration and higher-order operations on transfinite ordinals - by GFR - 02/26/2008, 09:33 AM RE: Tetration and higher-order operations on transfinite ordinals - by quickfur - 03/28/2008, 10:55 PM RE: Tetration and higher-order operations on transfinite ordinals - by bo198214 - 03/29/2008, 09:58 AM RE: Tetration and higher-order operations on transfinite ordinals - by quickfur - 03/29/2008, 04:01 PM RE: Tetration and higher-order operations on transfinite ordinals - by quickfur - 08/16/2008, 01:58 AM

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