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 |
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Keywords and phrases: | cardinal invariants, reals, pcf theory, null sets, meager sets, Baire space, additivity} |

Subjects: | 03E17 Cardinal characteristics of the continuum 03E04 Ordered sets and their cofinalities; pcf theory 03E35 Consistency and independence results |

Divisions: | Research Divisions > Set theory and general topology |

Last Modified: | 13 Jan 2011 14:17 |

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- Pcf theory and cardinal invariants of the reals. (deposited 10 Jan 2011 16:08)
- Pcf theory and cardinal invariants of the reals. (deposited 13 Jan 2011 14:17)
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- Pcf theory and cardinal invariants of the reals. (deposited 13 Jan 2011 14:17)

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