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

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

1992-01-15

arxiv.org/abs/math/9201250v1

Math. Japon. 37 (1992), 385--400

Mathematics

Logic

Scientific paper

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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