### Strong dichotomy of cardinality

by Shelah. [Sh:664]

Results in Math, 2001

A usual dichotomy is that in many cases, reasonably definable
sets, satisfy the CH, i.e. if they are uncountable they have
cardinality continuum. A strong dichotomy is when: if the
cardinality is infinite it is continuum as in [Sh:273]. We are
interested in such phenomena when lambda = aleph_0 is replaced by
lambda regular uncountable and also by lambda = beth_omega or
more generally by strong limit of cofinality aleph_0 .

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