THE MEASURE ALGEBRA DOES NOT ALWAYS EMBED

THE MEASURE ALGEBRA DOES NOT ALWAYS EMBED
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测度代数并不总是嵌入

DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
K. P. Hart
K. P. Hart
中科院分区：
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文献类型：
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作者：
A. Dow;K. P. Hart

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本文的目的是证明以下结果。主要定理。开放着色公理表明测度代数不能嵌入布尔代数P(N)/fin中。我们所说的“测度代数”是指实线的Borel集合的σ-代数与测度为零的集合的理想之商。除了纯粹的好奇心之外，人们对测度代数是否可以嵌入到P(N)/fin中有各种各样的兴趣。一个原因是人们对确定P(N)/fin的子代数非常感兴趣。在这个方向上最早和最具影响力的结果之一是Parovi - cenko的定理，它指出每个大小为λ的布尔代数
IntroductionThe aim of this paper is to prove the following result.Main Theorem. The Open Colouring Axiom implies that the measure algebracannot be embedded into the Boolean algebra P(N)/fin.By ‘the measure algebra’ we mean the quotient of the σ-algebra of Borel sets ofthe real line by the ideal of sets of measure zero.There are various reasons, besides sheer curiosity, why it is of interest to knowwhether the measure algebra can be embedded into P(N)/fin. One reason is thatthere is great interest in determining what the subalgebras of P(N)/fin are. Oneof the earliest and most influential result in this direction is Paroviˇcenko’s theoremfrom [11], which states that every Boolean algebra of size ℵ