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01216nam a2200193Ia 4500 |
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10.1016-j.apal.2022.103161 |
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220718s2022 CNT 000 0 und d |
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|a 01680072 (ISSN)
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| 245 |
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|a The spectrum of independence, II
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| 260 |
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|b Elsevier B.V.
|c 2022
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| 856 |
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|z View Fulltext in Publisher
|u https://doi.org/10.1016/j.apal.2022.103161
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|a We study the set sp(i)={|A|:A⊆[ω]ω is a maximal independent family}, referred to as the spectrum of independence. We develop a forcing notion, which allows us to adjoin a maximal independent family of arbitrary cardinality, and so in particular of cardinality ℵω. Moreover, given an arbitrary set Θ of uncountable cardinals, our techniques allow to obtain a cardinal preserving generic extension in which Θ⊆sp(i), thus showing that sp(i) can be arbitrarily large. For finite Θ, as well as certain countably infinite Θ, we can obtain a precise equality, i.e. models of sp(i)=Θ. © 2022 The Author(s)
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|a Combinatorial cardinal characteristics
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|a Consistency
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|a Independent families
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|a Spectrum
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|a Fischer, V.
|e author
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|a Shelah, S.
|e author
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| 773 |
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|t Annals of Pure and Applied Logic
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