# THE SOLIDITY AND NONSOLIDITY OF INITIAL SEGMENTS OF THE CORE MODEL

@article{Fuchs2018THESA,
title={THE SOLIDITY AND NONSOLIDITY OF INITIAL SEGMENTS OF THE CORE MODEL},
author={Gunter Fuchs and Ralf Schindler},
journal={The Journal of Symbolic Logic},
year={2018},
volume={83},
pages={920 - 938}
}
• Published 1 September 2018
• Mathematics
• The Journal of Symbolic Logic
Abstract It is shown that $K|{\omega _1}$ need not be solid in the sense previously introduced by the authors: it is consistent that there is no inner model with a Woodin cardinal yet there is an inner model W and a Cohen real x over W such that $K|{\omega _1}\,\, \in \,\,W[x] \setminus W$. However, if ${0^{\rm{\P}}}$ does not exist and $\kappa \ge {\omega _2}$ is a cardinal, then $K|\kappa$ is solid. We draw the conclusion that solidity is not forcing absolute in general, and that under the…
2 Citations

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The main result here is that if there is an inner model with a Woodin cardinal, then the solid core of a model of set theory is a fine-structural extender model.

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