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}
}
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… 
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INNER MODEL THEORETIC GEOLOGY

TLDR
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.

JSL volume 83 issue 4 Cover and Back matter

References

SHOWING 1-10 OF 11 REFERENCES

INNER MODEL THEORETIC GEOLOGY

TLDR
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.

Increasing u2 by a stationary set preserving forcing

TLDR
It is shown that if the nonstationary ideal on ω1 is precipitous and exists, then there is a stationary set preserving forcing which increases .

The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal

TLDR
The second edition of a well-established monograph on the identification of a canonical model in which the Continuum Hypothesis is false is updated to take into account some of the developments in the decade since the first edition appeared.

Σ31 absoluteness and the second uniform indiscernible

We show that that if every real has a sharp and there are Δ21-definable prewellorderings of ℝ of ordinal ranks unbounded inω2, then there is an inner model for a strong cardinal. Similarly, assuming

A criterion for coarse iterability

TLDR
The main result of this paper is the following theorem: If M is linearly coarsely iterable via hitting F and its images, and M* is a linear iterate of M as in (a), then M is coarsely Iterable with respect to iteration trees which do not use the top extender of M* and its image.

Inner Models and Large Cardinals

Preface Fine Structure Extenders and Coherent Structures Fine Ultrapowers Mice and Iterability Solidity and Condensation Extender Models The Core Model One Strong Cardinal Overlapping Extenders

Long projective wellorderings

On some problems of Mitchell, Welch, and Vickers, handwritten notes

  • 1990

On some problems of Mitchell, Welch, and Vickers

  • Handwritten notes,
  • 1990

Jensen . The core model for nonoverlapping extenders