Re: Tarski (complete and consistent?)

[Chuck Britton <britton@odie.ncssm.edu>]

> wow!
> Any references available?

	Cambridge Press
	http://www.cup.org/Titles/45/0521457041.html
	A recent (within two? years) cover story in the New American Scientist
	An OLD issue of Sci. Am. (from the 60's,
				sorry our CD index is tied up now)
	http://www.paias.com/paiasemw.htm#BANACH
	http://math.bu.edu/people/jeffs/mathematicians.html
	http://studwww.rug.ac.be/~hvernaev/FAQ/node37.html quote follows
	``Banach and Tarski had hoped that the physical absurdity of this
theorem would encourage mathematicians to discard AC.(Axiom of Choice)
They were dismayed when the response of the math community was `Isn't AC
great? How else could we get such counterintuitive results?' ''
	A quick 'net' search turns up hundreds of 'reputable' (mathematical)
	sites.


> M.A.Santos
> msantos@etse.urv.es
> > twayburn@juno.com (Thomas L Wayburn) quotes:
> > > If the axiom system of a deductive theory is complete, and if any
> > > sentence which can be formulated but not proved within that theory is
> > > added to the system, then the axiom system extended in this manner is no
> > > longer consistent. - Tarski, Alfred, *Introduction to Logic ...*, Oxford,
> > > New York (1994), p. 133.
> >
> >
> > And anyone who is 'into' axiomatic mathematics needs to read up on the
> > Banach-Tarksi results that clearly show that our current understanding of
> > differential calculus leads to the result that a shperical set of points
> > with size equal to the sun can be dissected into a finite number of subsets
> > that can be reassembled into a sphere the size of a pea (or any other size)
> > with no points left out, overlapping etc.
> >
> >
> > hmmm.

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Chuck Britton  					Education is what is left when
britton@odie.ncssm.edu  			you have forgotten everything
North Carolina School of Science & Math		you learned in school.
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