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 b₁ b₂ Ba+1 c₁ cardinality chain CLAIM closed unbounded co-complete cofinal commutative consider construction contradiction Corollary countable set countable subalgebras definition denote dense elementary substructures embeddings exists filtered Boolean algebras filtration finite intersection property follows free Boolean algebra Fuchino functor hence homomorphism implies increasing sequence induction infinite intersection isomorphic L-formula Lemma limit ordinal mapping maximal minimal N₁ N2-projectively filtered non-zero elements o-filtered pairwise disjoint partially ordered set preserves prime ideal projective Boolean algebras Proof Proposition prove rc-filtered Boolean algebras rc-filtration rc-skeleton regular cardinal regular ideal regular skeleton regularly filtered relatively complete subalgebras satisfies the ccc Ščepin set theory subset substructures of Hy SUCCESSOR STEP surjective Theorem topological ultrafilter uncountable w₁ weakly projective algebras well-ordered yields