Pcf theory and cardinal invariants of the reals

Lajos Soukup

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arXiv · 1006.1808

Pcf theory and cardinal invariants of the reals

Lajos Soukup

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Abstract

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 cardinals can be ADD(I) in some c.c.c generic extension iff A=pcf(A).

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BibTeX RIS

Lajos Soukup. 2010-06-09. Pcf theory and cardinal invariants of the reals. https://arxiv.org/abs/1006.1808

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