# Pcf theory and cardinal invariants of the reals

Soukup, Lajos (2010) Pcf theory and cardinal invariants of the reals. CMUC . (In Press)

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## Abstract

The additivity spectrum of an ideal is the set of all regular cardinals such that there is an increasing chain with .
We investigate which set of regular cardinals can be the additivity spectrum of certain ideals.
Assume that or , where denotes the -ideal generated by the compact subsets of the Baire space , and is the ideal of the null sets.
We show that if is a non-empty progressive set of uncountable regular cardinals and , then in some c.c.c generic extension of the ground model. On the other hand, we also show that if is a countable subset of , then .
For countable sets these results give a full characterization of the additivity spectrum of : a non-empty countable set of uncountable regular cardinals can be in some c.c.c generic extension iff .

Item Type: Article cardinal invariants, reals, pcf theory, null sets, meager sets, Baire space, additivity} 03E17 Cardinal characteristics of the continuum03E04 Ordered sets and their cofinalities; pcf theory03E35 Consistency and independence results Research Divisions > Set theory and general topology 13 Jan 2011 14:17

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