Generic saturation

DOI10.2307/2586594zbMATH Open0906.03052arXivmath/9609202OpenAlexW3037313481MaRDI QIDQ4391429

Sy-David Friedman

Publication date: 4 February 1999

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Abstract: Assuming that ORD is $omega+omega$-Erd"os we show that if a class forcing amenable to $L$ (an $L$-forcing) has a generic then it has one definable in a set-generic extension of $$. In fact we may choose such a generic to be {it periodic} in the sense that it preserve the indiscernibility of a final segment of a periodic subclass of the Silver indiscernibles, and therefore to be {it almost codable} in the sense that it is definable from a real which is generic for an $L$-forcing (and which belongs to a set-generic extension of $$).

Full work available at URL: https://arxiv.org/abs/math/9609202

zbMATH Keywords

\(\alpha\)-Erdős cardinal\(\lambda_0,\lambda\)-periodic class forcingset-generic extensionSilver's indiscernibles

Mathematics Subject Classification ID

Inner models, including constructibility, ordinal definability, and core models (03E45) Large cardinals (03E55) Other aspects of forcing and Boolean-valued models (03E40)

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