Le 11-mai-07, à 02:19, Brent Meeker a écrit :

>
> Thanks, Bruno.  I did know that - just forgot because it's been a long 
> time.  I don't think it's related to Brouwer's fixed point theorem 
> though: that assumes a continuous topology.  But I see what you mean 
> by a fixed point of computation.

Thanks for saying.

In theoretical computer science they are two "recursion theorems", or 
fixed point theorems; the first one is more easy to relate to topology, 
and the second one, well, it is harder to say. It is easier to define 
topology on the "total computable function or functionals" (although 
not recursively enumerable) that on the partial recursive functions 
(the Fi, although recursively enumerable). The first topologies are 
related to the first person, (I think) and intuitionistic logic, the 
second are related to, hmmmm ...., the whole truth about numbers, or 
platonia (the place where universal (or not) machines are relatively 
confronted to *other* universal (or not) machines with hopefully 
intelligible statistics.

Bruno

http://iridia.ulb.ac.be/~marchal/


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