Nearly projective Boolean algebras
The 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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Setting the stage
rcfiltered Boolean algebras
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Aa+i assertion Assume atomless atoms Ba+i cardinality chain characterization Claim closed unbounded co-complete cofinal commutative consider construction contradiction Corollary countable set countable subalgebras defined definition denote dense desired diagram elementary substructures embeddings exists expA filtered Boolean algebras filtration finite intersection property finite union follows free algebra free Boolean algebra Fuchino functor hence holds homomorphism implies increasing sequence infinite intersection isomorphic jree L-formula limit ordinal Ma+i mapping maximal minimal non-zero elements pairwise disjoint partially ordered partially ordered set preserves prime ideal projective Boolean algebras Proof Proposition prove rc-filtered Boolean algebras rc-filtration rc-skeleton reader regular cardinal regular ideal regular skeleton regularly filtered relatively complete subalgebras result satisfies the ccc Scepin set theory spaces successor step surjective Theorem topological ultrafilter v(ai weakly projective algebras well-ordered witness yields