2008‱Transactions of the American Mathematical SocietyOpen access

đŒ[𝜔₂] can be the nonstationary ideal on Ci`(𝜔₁)

William Mitchell

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Abstract

We answer a question of Shelah by showing that it is consistent that every member of I [ ω 2 ] ∩ Cof ⁥ ( ω 1 ) I[\omega _2]\cap \operatorname {Cof}(\omega _1) is nonstationary if and only if it is consistent that there is a Îș + \kappa ^+ -Mahlo cardinal Îș \kappa .

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We answer a question of Shelah by showing that it is consistent that every member of I [ ω 2 ] ∩ Cof ⁥ ( ω 1 ) I[\omega _2]\cap \operatorname {Cof}(\omega _1) is nonstationary if and only if it is consistent that there is a Îș + \kappa ^+ -Mahlo cardinal Îș \kappa .

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We answer a question of Shelah by showing that it is consistent that every member of I [ ω 2 ] ∩ Cof ⁥ ( ω 1 ) I[\omega _2]\cap \operatorname {Cof}(\omega _1) is nonstationary if and only if it is consistent that there is a Îș + \kappa ^+ -Mahlo cardinal Îș \kappa .

Key concepts: Mathematics, Ideal (ethics), Calculus (dental), Mathematical economics, Epistemology, Medicine, Philosophy, Dentistry

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