Characterization of □κ in Core Models

We present a general construction of a □κ-sequence in Jensen's fine structural extender models. This construction yields a local definition of a canonical □κ-sequence as well as a characterization of those cardinals κ, for which the principle □κ fails. Such cardinals are called subcompact and can be described in terms of elementary embeddings. Our construction is carried out abstractly, making use only of a few fine structural properties of levels of the model, such as solidity and condensation.

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