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Re: Prime Interger Topology
Posted:
Oct 21, 2013 4:24 AM


On Sun, 20 Oct 2013, fom wrote: > On 10/20/2013 9:58 PM, William Elliot wrote: > > > > Why relations? Aren't functiosn used to manage the undue complexity of > > relations? > > This is the pair coding function from Goedel's > lemma in Kaye's "Models of Peano Arithemtic" > > < x, y > = [ ( x + y )( x + y + 1) / 2 ] + y > > Given any "definite" model of my axioms, I > could collapse the relations into sets of > numbers arithmetically. > > Those sets probably could not be represented recursively.
(0,0) = 0 (x+1, 0) = (x + 1)(x + 2)/2 = x(x + 1)/2 + x + 1 = (x,0) + x + 1
(x, y+1) = (x + y + 1)(x + y + 2)/2 + y + 1 = (x + y)(x + y + 1)/2 + x + y + 1 + y + 1 = (x,y) + x + y + 2



