FOM: history of AC
Martin Davis
martin at eipye.com
Thu May 11 15:04:35 EDT 2000
Arnon Avron wrote (referring to Friedman's comparison of alrge cardianl
axioms with AC):
>I believe that the comparison with AC here is inappropriate. The big
>difference
>is that AC has implicitly been used by mathematicians (at least in a weak
>form, like DC) long before it was explicitly formulated by Zermelo and Russel.
This history wasn't so smooth. See Moore's excellent monograph "Zermelo's
Axiom of Choice". Peano's first reaction to AC was that it was evidently
false. The French "finitists" (Borel, Lebesgue, de la Valle Poussin), made
a big point of avoiding it. De la Valle Poussin's monograph on Lebesgue
integration (from which I learned the subject) in its second edition even
refused to state the theorem that the union of a countable set of countable
sets is countable without including the proviso that the implied mappings
are explicitly given.
Martin
Martin Davis
Visiting Scholar UC Berkeley
Professor Emeritus, NYU
martin at eipye.com
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http://www.eipye.com
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