Journal of Mathematical Logic 4 (01):1-72 (2004)

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.
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DOI 10.1142/S0219061304000310
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References found in this work BETA

Strong Axioms of Infinity and Elementary Embeddings.Robert M. Solovay - 1978 - Annals of Mathematical Logic 13 (1):73.
Set Theory.Thomas Jech - 1981 - Journal of Symbolic Logic.
Squares, Scales and Stationary Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
Combinatorial Principles in the Core Model for One Woodin Cardinal.Ernest Schimmerling - 1995 - Annals of Pure and Applied Logic 74 (2):153-201.
Constructibility.Keith J. Devlin - 1987 - Journal of Symbolic Logic 52 (3):864-867.

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Citations of this work BETA

Simultaneous Stationary Reflection and Square Sequences.Yair Hayut & Chris Lambie-Hanson - 2017 - Journal of Mathematical Logic 17 (2):1750010.
Stacking Mice.Ronald Jensen, Ernest Schimmerling, Ralf Schindler & John Steel - 2009 - Journal of Symbolic Logic 74 (1):315-335.
A Microscopic Approach to Souslin-Tree Constructions, Part I.Ari Meir Brodsky & Assaf Rinot - 2017 - Annals of Pure and Applied Logic 168 (11):1949-2007.
$K$ Without the Measurable.Ronald Jensen & John Steel - 2013 - Journal of Symbolic Logic 78 (3):708-734.

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