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Changing cardinal invariants of the reals without changing cardinals or the reals

Heike Mildenberger

Journal of Symbolic Logic 63 (2):593-599 (1998)

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Changing cardinal characteristics without changing ω-sequences or cofinalities.Heike Mildenberger & Saharon Shelah - 2000 - Annals of Pure and Applied Logic 106 (1-3):207-261.details We show: There are pairs of universes V1V2 and there is a notion of forcing PV1 such that the change mentioned in the title occurs when going from V1[G] to V2[G] for a P-generic filter G over V2. We use forcing iterations with partial memories. Moreover, we implement highly transitive automorphism groups into the forcing orders. Download Export citation Bookmark 2 citations
(1 other version)Controlling cardinal characteristics without adding reals.Martin Goldstern, Jakob Kellner, Diego A. Mejía & Saharon Shelah - 2021 - Journal of Mathematical Logic 21 (3):2150018.details We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new [Formula: see text]-sequences (for some regular [Formula: see text]). As an application, we show that consistently the following cardinal characteristics can be different: The (“independent”) characteristics in Cichoń’s diagram, plus [Formula: see text]. (So we get thirteen different values, including [Formula: see text] and continuum). We also give constructions to alternatively separate other MA-numbers (instead of [Formula: see text]), namely: MA for [Formula: see (...) Download Export citation Bookmark
(1 other version)Controlling cardinal characteristics without adding reals.Martin Goldstern, Jakob Kellner, Diego A. Mejía & Saharon Shelah - 2020 - Journal of Mathematical Logic 21 (3).details We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new <κ-sequences. As an application, we show that consistently the followi... Download Export citation Bookmark

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