The tree property at double successors of singular cardinals of uncountable cofinality with infinite gaps
نویسندگان
چکیده
Assume that κ and λ are respectively strong weakly compact cardinals with λ>κ. Fix Θ≥λ a cardinal cof(Θ)>κ cof(δ)=δ<κ. Assuming the GCH≥κ holds, we construct generic extension of universe where is limit cardinal, cof(κ)=δ, 2κ=Θ TP(κ++) holds. This extends main result [5] for uncountable cofinalities.
منابع مشابه
The tree property at double successors of singular cardinals of uncountable cofinality
Assuming the existence of a strong cardinal κ and a measurable cardinal above it, we force a generic extension in which κ is a singular strong limit cardinal of any given cofinality, and such that the tree property holds at κ++.
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2021
ISSN: ['0168-0072', '1873-2461']
DOI: https://doi.org/10.1016/j.apal.2020.102853