The additivity of porosity ideals
英文摘要:
We show that several sigma-ideals related to porous sets have additivity omega_1 and cofinality 2^omega. This answers a question addressed by Miroslav Repick'y.
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Jörg Brendle
We show that several sigma-ideals related to porous sets have additivity omega_1 and cofinality 2^omega. This answers a question addressed by Miroslav Repick'y.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
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$σ$-Porosity of Certain Ideals
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We study the relationship between the sigma-ideal generated by closed measure zero sets and the ideals of null and meager sets. We show that the additivity of the ideal of closed measure zero sets is not bigger than covering for category. As a consequence we get that the additivity of the ideal of closed measure zero sets is equal to the additivity of the ideal of meager sets.
Yorioka [J. Symbolic Logic 67(4):1373-1384, 2002] introduced a class of ideals (parametrized by reals) on the Cantor space to prove that the relation between the size of the continuum and the cofinality of the strong measure zero ideal on the real line cannot be decided in ZFC. We construct a matrix iteration of ccc posets to force that, for many ideals in that class, their associated cardinal invariants (i.e. additivity, covering, uniformity and cofinality) are pairwise different. In addition, we show that, consistently, the additivity and cofinality of Yorioka ideals does not coincide with t…
The additivity spectrum ADD(I) of an ideal I is the set of all regular cardinals kappa such that there is an increasing chain {A_alpha:alpha<kappa\} in the ideal I such that the union of the chain is not in I. We investigate which set A of regular cardinals can be the additivity spectrum of certain ideals. Assume that I=B or I=N, where B denotes the sigma-ideal generated by the compact subsets of the Baire space omega^omega, and N is the ideal of the null sets. For countable sets we give a full characterization of the additivity spectrum of I: a non-empty countable set A of uncountable regular…
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