### Factor = quotient, uncountable Boolean algebras, number of endomorphism and width

by Shelah. [Sh:397]

Math Japonica, 1992

We prove that assuming suitable cardinal arithmetic, if
B is a Boolean algebra every homomorphic image of which is
isomorphic to a factor, then B has locally small density. We
also prove that for an (infinite) Boolean algebra B, the
number of subalgebras is not smaller than the number of
endomorphisms, and other related inequalities. Lastly we deal
with the obtainment of the supremum of the cardinalities of sets
of pairwise incomparable elements of a Boolean algebra.

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