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A model with a measurable which does not carry a normal measure

Eilon Bilinsky & Moti Gitik

Archive for Mathematical Logic 51 (7-8):863-876 (2012)

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Combinatorial properties and dependent choice in symmetric extensions based on Lévy collapse.Amitayu Banerjee - 2022 - Archive for Mathematical Logic 62 (3):369-399.details We work with symmetric extensions based on Lévy collapse and extend a few results of Apter, Cody, and Koepke. We prove a conjecture of Dimitriou from her Ph.D. thesis. We also observe that if V is a model of $$\textsf {ZFC}$$ ZFC, then $$\textsf {DC}_{<\kappa }$$ DC < κ can be preserved in the symmetric extension of V in terms of symmetric system $$\langle {\mathbb {P}},{\mathcal {G}},{\mathcal {F}}\rangle $$ ⟨ P, G, F ⟩, if $${\mathbb {P}}$$ P is $$\kappa $$ (...) Download Export citation Bookmark
Controlling the number of normal measures at successor cardinals.Arthur W. Apter - 2022 - Mathematical Logic Quarterly 68 (3):304-309.details We examine the number of normal measures a successor cardinal can carry, in universes in which the Axiom of Choice is false. When considering successors of singular cardinals, we establish relative consistency results assuming instances of supercompactness, together with the Ultrapower Axiom (introduced by Goldberg in [12]). When considering successors of regular cardinals, we establish relative consistency results only assuming the existence of one measurable cardinal. This allows for equiconsistencies. Download Export citation Bookmark

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