random (fwd)

David C. Ullrich ullrich at math.okstate.edu
Sun Jun 3 17:45:09 CEST 2001


On Sat, 02 Jun 2001 12:51:10 -0400, Lulu of the Lotus-Eaters
<mertz at gnosis.cx> wrote:

>Coming, admittedly, a bit late to the conversation on this topic, I'm
>surprised to find Alex a bit too dedicated to his point... and making a
>few errors about which he knows better:
>
>Someone wrote:

Those anonymous posters can be irritating.
[...]
>
>The Incompleteness of Arithmetic simply says:
>
>   ANY (finite axiomatic) system powerful enough to model arithmetic
>   must contain statements that are not derivable from the axioms of
>   that system.
>
>So, for example, ZF can model the Peano axioms, and therefore gets stung
>by the incompleteness bug.  But this much leaves open the possibility
>that ZF is strictly more powerful than arithmetic.  (question though:
>is this actually true of ZF--can it be modelled with the Peano axioms?).

No. (Um, don't ask me to prove that, but it seems clear.)


David C. Ullrich
*********************
"Sometimes you can have access violations all the 
time and the program still works." (Michael Caracena, 
comp.lang.pascal.delphi.misc 5/1/01)



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