CHARACTERIZATION OF □_κ IN CORE MODELS

Abstract

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.