[FOM] From theorems of infinity to axioms of infinity
Sam Sanders
sasander at cage.ugent.be
Sat Mar 23 04:13:31 EDT 2013
Eskew and Weaver are debating "set theory vs predicative systems".
Weaver has made a subtle conceptual point about why the power set axiom is unacceptable.
I am afraid this point would be mostly lost on most mainstream mathematicians, however.
At the very least, they would not "immediately get it".
Eskew mentions examples of where set theory connects directly with mainstream mathematics.
He mentioned something like "If inaccessible cardinals are consistent, then AC is needed to build non-measurable sets".
As anecdotal evidence, my math department shares a building with an engineering math department. There
are a number of analysts in both departments who find Monroe's example interesting, as it
lays to rest questions they have asked themselves for years about non-measurable sets.
Best,
Sam Sanders
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