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On closed unbounded sets consisting of former regulars

Journal of Symbolic Logic 64 (1):1-12 (1999)

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Universal partial indestructibility and strong compactness.Arthur W. Apter - 2005 - Mathematical Logic Quarterly 51 (5):524-531.details For any ordinal δ, let λδ be the least inaccessible cardinal above δ. We force and construct a model in which the least supercompact cardinal κ is indestructible under κ-directed closed forcing and in which every measurable cardinal δ < κ is < λδ strongly compact and has its < λδ strong compactness indestructible under δ-directed closed forcing of rank less than λδ. In this model, κ is also the least strongly compact cardinal. We also establish versions of this result (...) Download Export citation Bookmark 1 citation
A cardinal preserving extension making the set of points of countable V cofinality nonstationary.Moti Gitik, Itay Neeman & Dima Sinapova - 2007 - Archive for Mathematical Logic 46 (5-6):451-456.details Assuming large cardinals we produce a forcing extension of V which preserves cardinals, does not add reals, and makes the set of points of countable V cofinality in κ+ nonstationary. Continuing to force further, we obtain an extension in which the set of points of countable V cofinality in ν is nonstationary for every regular ν ≥ κ+. Finally we show that our large cardinal assumption is optimal. Download Export citation Bookmark
A Gitik iteration with nearly Easton factoring.William Mitchell - 2003 - Journal of Symbolic Logic 68 (2):481-502.details We reprove Gitik's theorem that if the GCH holds and o(κ) = κ + 1 then there is a generic extension in which κ is still measurable and there is a closed unbounded subset C of κ such that every $\nu \in C$ is inaccessible in the ground model. Unlike the forcing used by Gitik. the iterated forcing $R_{\lambda +1}$ used in this paper has the property that if λ is a cardinal less then κ then $R_{\lambda + 1}$ can (...) Download Export citation Bookmark
Homogeneous changes in cofinalities with applications to HOD.Omer Ben-Neria & Spencer Unger - 2017 - Journal of Mathematical Logic 17 (2):1750007.details We present a new technique for changing the cofinality of large cardinals using homogeneous forcing. As an application we show that many singular cardinals in [Formula: see text] can be measurable in HOD. We also answer a related question of Cummings, Friedman and Golshani by producing a model in which every regular uncountable cardinal [Formula: see text] in [Formula: see text] is [Formula: see text]-supercompact in HOD. Download Export citation Bookmark 5 citations

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