  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 .
