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Guessing more sets

Annals of Pure and Applied Logic 166 (10):953-990 (2015)

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  1. Applications of Pcf Theory to the Study of Ideals On.Pierre Matet - 2022 - Journal of Symbolic Logic 87 (3):967-994.
    Let $\kappa $ be a regular uncountable cardinal, and a cardinal greater than or equal to $\kappa $. Revisiting a celebrated result of Shelah, we show that if is close to $\kappa $ and (= the least size of a cofinal subset of ) is greater than, then can be represented (in the sense of pcf theory) as a pseudopower. This can be used to obtain optimal results concerning the splitting problem. For example we show that if and, then no (...)
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  • Meeting numbers and pseudopowers.Pierre Matet - 2021 - Mathematical Logic Quarterly 67 (1):59-76.
    We study the role of meeting numbers in pcf theory. In particular, Shelah's Strong Hypothesis is shown to be equivalent to the assertion that for any singular cardinal σ of cofinality ω, there is a size σ + collection Q of countable subsets of σ with the property that for any infinite subset a of σ, there is a member of Q meeting a in an infinite set.
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  • On the ideal J[κ].Assaf Rinot - 2022 - Annals of Pure and Applied Logic 173 (2):103055.
  • When P(λ) (vaguely) resembles κ.Pierre Matet - 2021 - Annals of Pure and Applied Logic 172 (2):102874.
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  • The secret life of μ-clubs.Pierre Matet - 2022 - Annals of Pure and Applied Logic 173 (9):103162.
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  • Towers and clubs.Pierre Matet - 2021 - Archive for Mathematical Logic 60 (6):683-719.
    We revisit several results concerning club principles and nonsaturation of the nonstationary ideal, attempting to improve them in various ways. So we typically deal with a ideal J extending the nonstationary ideal on a regular uncountable cardinal \, our goal being to witness the nonsaturation of J by the existence of towers ).
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