K-theory and sets

[Ignacio Añón]

M Eskew wrote:


The consistency of an arbitrarily large value of the continuum was
established definitively by Cohen. I guarantee you that Todorcevic fully
accepts this result. He is a master of forcing. He might see forcing axioms
like PFA that imply the value of the continuum to be aleph2 as Platonically
true, while acknowledging that different scenarios are consistent.


You're right. Most of us would agree that the consistency of arbitrary
large values for the continuum was formally settled by Cohen, although some
might interpret this result as trivial, particularly since forcing methods,
or any such technique to construct denumerable models, is known to be
equivalent to logical boolean valued models, and hence these models seem to
be preeminently determined by certain concrete, new, stronger than Mahlo
infinity axioms that imply, naturally, the existence of non constructible
sets, but imply so in a quite direct, concrete, limited, non-arbitrary
way...

My point was that certain set theorists are interested in finding out which
are the minimal, consistent, models where the limit is aleph 2, while
others see no value in this. Here our paths separate...

Best
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