random (fwd)

David C. Ullrich ullrich at math.okstate.edu
Sun Jun 3 11:45:09 EDT 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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