Titlebook: Cardinal Functions on Boolean Algebras; J. Donald Monk Book 1990 Springer Basel AG 1990 algebra.Boolean algebra.cardinal function.function

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Lectures in Mathematics. ETH Zürichhttp://image.papertrans.cn/c/image/221847.jpg

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negligence

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https://doi.org/10.1007/0-387-31609-4A BA . is said to satisfy the . if every disjoint subset of . has power < .. Thus for . non-limit, this is the same as saying that the cellularity of . is < .. Of most interest is the ..-chain condition, called ccc for short (countable chain condition). We shall return to it below.

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https://doi.org/10.1007/0-387-31609-4We begin with some equivalents of this notion. A set . of non-zero elements of a BA . is said to be . provided that it satisfies the finite intersection property. And . is called . if .{0} is the union of . centered sets.

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Undergraduate Texts in MathematicsRecall that Length . is the sup of cardinalities of subsets of . which are simply ordered by the Boolean ordering. For references see the beginning of section 2. The analysis of Length is similar to that for Depth; many of the proofs are similar, but there are some differences.

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https://doi.org/10.1007/0-387-31609-4There is a lot of information about independence in Part I of the Handbook. An even more extensive account is in Monk [83].

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