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In this paper we isolate a new criterion for when a given real $x$ is generic over $L$ in terms of $x$'s capability of lifting elementary embeddings of initial segments of $L$.
Characterization of generic extensions of models of set theory
Bukowský, L · 1973
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The extender algebra and 𝚺 1 2 \boldsymbol{\Sigma}^{2}_{1} -absoluteness
Farah, I
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Preserving levels of projective determinacy by tree forcings
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