A Characterization of (κ) in Extender Models
نویسندگان
چکیده
We prove that, in any fine structural extender model with Jensen’s λ-indexing, there is a (κ)-sequence if and only if there is a pair of stationary subsets of κ ∩ cof(< κ) without common reflection point of cofinality < κ which, in turn, is equivalent to the existence of a family of size < κ of stationary subsets of κ ∩ cof(< κ) without common reflection point of cofinality < κ. By a result of Burke/Jensen, κ fails whenever κ is a subcompact cardinal. Our result shows that in extender models, it is still possible to construct a canonical (κ)-sequence where κ is the first subcompact.
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