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Ikegami and Schlicht proposed a principle, namely generic absoluteness, which is stated below using Hamkins' and Lowe's terminology: Working in $ZF$: (Generic Absoluteness): For all formulas in ...

Definition: Let $\kappa$ be an $\aleph$ cardinal, we say that $\langle f_\alpha\colon\alpha\to\kappa\mid\alpha<\kappa^+\rangle$ is a ladder if every $f_\alpha$ is injective. Equivalently this is ...