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Results tagged with inner-model-theory
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user 4753
The study of canonical inner models for large cardinal hypotheses, with particular attention to their fine structure theory, and iterability issues.
5
votes
Accepted
Showing that $\alpha$ isn't a cardinal in $J_{\alpha+1}^{\vec E}$ for a fine extender sequen...
We know that $\alpha = (\nu^{+})^{Ult(J^{\vec{E}}_{\alpha}, E_{\alpha})}$ and that $i_{E_{\alpha}} (\kappa) > \nu$, where $i_{E_{\alpha}}$ denotes the ultrapower embedding. Thus working in $Ult(J^{E_{ …
- 2,180
3
votes
Accepted
Preservation of Woodinness when it overlaps the active extender
The Woodiness of $\delta$ in $\mathcal{J}^{\mathcal{M}}_{lh(E)}$ is witnessed by a bunch of extenders, which are either on the $\vec{E}$ sequence of $\mathcal{M}$ or are definable from elements of $\v …
- 2,180
6
votes
1
answer
320
views
Elementary chains in forcing extensions of $M_1$
Let $M_1$ be the canonical inner model with one Woodin cardinal $\delta$. Now suppose that $\mathbb{P}$ is a forcing notion of size $< \delta$, which preserves $\omega_1$ and that $G$ is a generic fi …
- 2,180