Sep 3, 2022 · Since DC holds in L ( R ) and E is countably closed, it follows that both R and ω 1 are preserved under E –forcing.
We present conditions under which one can generically add new elements to L ( R ) L(\mathbb {R}) L(R) and obtain a model of ZF+AD+DC.
Jan 14, 2017 · I'm interested in when (FC)C is compatible with large cardinals - specifically, a proper class of Woodins - and when it adds large cardinal ...
On forcing over L(\mathbb {R})$$ · journal article · research article · Published by Springer Nature in Archive for Mathematical Logic.
Mar 3, 2000 · Abstract: We present two ways in which the model L({\mathbb R}) is canonical assuming the existence of large cardinals.
In particular, ZF + AD + V = L(ℝ) proves that for every nontrivial forcing \( \mathbb{P}\in {L_\Theta }\left(\mathbb{R}\right),{1_\mathbb{P}}{ \Vdash _\mathbb{P}}\ ...
Sep 21, 2017 · Since L(R) is definable we know that j restricts to an elementary embedding L(R)→L(R), and that this embedding is nontrivial since κ∈L(R), being an ordinal.
top We show that in the presence of large cardinals proper forcings do not change the theory of with real and ordinal parameters and do not code any set of ...
Given that ⊧ L ( R ) ⊧ ZF + AD + DC , we present conditions under which one can generically add new elements to L ( R ) and obtain a model of ZF + AD + DC .
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Papers by Daniel Cunningham. Research paper thumbnail of On forcing over $$L(\mathbb {R} · On forcing over $$L(\mathbb {R})$$. Archive for Mathematical Logic.