AUC Philosophica et Historica (Acta Universitatis Carolinae Philosophica et Historica) is a multidisciplinary academic journal focused on the humanities with more than 50 years of tradition.
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AUC PHILOSOPHICA ET HISTORICA, Vol 2017 No 2 (2017), 27–32
Preserving measurability with Cohen iterations
Radek Honzík
DOI: https://doi.org/10.14712/24647055.2017.13
published online: 14. 11. 2017
abstract
We describe a weak version of Laver indestructibility for a μ-tall cardinal κ, μ > κ+, where “weaker” means that the indestructibility refers only to the Cohen forcing at κ of a certain length. A special case of this construction is: if μ is equal to κ+n for some 1 < n < ω, then one can get a model V∗ where κ is measurable, and its measurability is indestructible by Add(κ, α) for any 0 ≤ α ≤ κ+n (Theorem 3.3).
keywords: Cohen forcing; measurability
references (7)
1. Arthur W. Apter. Strong Cardinals can be Fully Laver Indestructible. Mathematical Logic Quarterly, 48: 499–507, 2002. CrossRef
2. James Cummings. A model in which GCH holds at successors but fails at limits. Transactions of the American Mahematical Society, 329(1): 1–39, 1992. CrossRef
3. James Cummings. Iterated forcing and elementary embeddings. In Matthew Foreman and Akihiro Kanamori, editors, Handbook of Set Theory, volume 2. Springer, 2010. CrossRef
4. James Cummings and Matthew Foreman. The tree property. Advances in Mathematics, 133(1): 1–32, 1998. CrossRef
5. Moti Gitik and Carmi Merimovich. Possible values for 2ℵn and 2ℵω . Annals of Pure and Applied Logic, 90(1–3): 193–241, 1997. CrossRef
6. Joel David Hamkins. Gap forcing. Israel Journal of Mathematics, 125(1): 237–252, 2001. CrossRef
7. Richard Laver. Making the supercompactness of κ indestructible under κ directed closed forcing. Israel Journal of Mathematics, 29(4): 385–388, 1978. CrossRef
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