Pcf theory and cardinal invariants of the reals
L Soukup�- arXiv preprint arXiv:1006.1808, 2010 - arxiv.org
arXiv preprint arXiv:1006.1808, 2010•arxiv.org
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�…
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�…
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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