Nearly Projective Boolean Algebras, Volume 1596The book is a fairly complete and up-to-date survey of projectivity and its generalizations in the class of Boolean algebras. Although algebra adds its own methods and questions, many of the results presented were first proved by topologists in the more general setting of (not necessarily zero-dimensional) compact spaces. An appendix demonstrates the application of advanced set-theoretic methods to the field. The intended readers are Boolean and universal algebraists. The book will also be useful for general topologists wanting to learn about kappa-metrizable spaces and related classes. The text is practically self-contained but assumes experience with the basic concepts and techniques of Boolean algebras. |
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a₁ Aa+1 assertion Assume atomless atoms b₁ b₂ Ba+1 c₁ cardinal chain characterization CLAIM closed and unbounded closed unbounded subset co-complete cofinal consider construction contradiction Corollary countable set countable subalgebras definition denote dense elementary substructures exists filtered Boolean algebras filtration finite union follows free algebra free Boolean algebra Fuchino functor Hence holds homomorphism implies increasing sequence infinite intersection isomorphic Koppelberg L-formula Lemma limit ordinal Ma+1 mapping maximal minimal N₁ N2-projectively filtered non-zero elements o-filtered pairwise disjoint partially ordered set Player prime ideal projective Boolean algebra Proposition prove rc-filtered Boolean algebras rc-filtration reader regular cardinal regular ideal regular skeleton regularly filtered relatively complete subalgebra Sa+1 satisfies the ccc Ščepin set theory spaces substructures of Hy SUCCESSOR STEP surjective T₁ topological ultrafilter uncountable w₁ weakly projective algebras well-ordered yields