[FOM] Criteria for New Axioms

[martdowd at aol.com]

Dmytro Taranovsky writes





but whose decisions are symbolic rather than

giving a license to silently omit the axioms in published theorems.

 

 I think mathematics will always be interested in whether a theorem of mathematics is provable in ZFC.  Indeed, this is a principle aspect of new axiom theory; ZFC can be extended, but this doesn't have much relevance to ordinary mathematics.

I'm in favor of a conservative approach.  Con(ZFC) is an acceptable new axiom.  The existence of inaccessible cardinals can be seen as not much stronger, and almost certainly true.  These methods can be extended, as can be found in papers of mine linked to in earlier postings of mine to FOM.

It seems unlikely to me that Woodin cardinals can be justified by these methods.  I think there is a strong case for V=L, and as work progresses the case may become stronger.

- Martin Dowd

 





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