Re: Paper and slides on indefiniteness of CH

Dear Sy,

If we are talking about ST in terms of its role as a foundation for or subfield of mathematics (Types 1 and 2) then we needn’t trouble ourvselves with this discussion of universes for ST and can hang our hats on what axioms of set theory are advantageous for the development of set theory and mathematics, as was done with AC and the Axiom of Infinity, for example.

Thanks for this clarification.  If all we care about is set theory as a branch of mathematics and set theory as it relates to the rest of mathematics, then we can stick with our familiar iterative picture of V and rely on extrinsic justifications of the familiar sort (unless the extrinsic evidence eventually leads us to prefer some sort of multiverse, in which case we’d shift to a new picture).  It’s only when we’re interested in further exploration of ‘the maximality of the set-concept’ that we need to engage in the HP (or the MP).

All best,

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