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The additivity spectrum ADD(I) of an ideal I is the set of all regularcardinals 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 additivityspectrum of certain ideals.  Assume that I=B or I=N, where B denotes the sigma-ideal generated by thecompact subsets of the Baire space omega^omega, and N is the ideal of the nullsets.  For countable sets we give a full characterization of the additivity spectrumof I: a non-empty countable set A of uncountable regular cardinals can beADD(I) in some c.c.c generic extension iff A=pcf(A).

Pcf theory and cardinal invariants of the reals