A stronger version of stationarity preserved under <κ-strategically closed forcing
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概要
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We introduce a normal filter F^<SIA>_κλ over P_κλ for an inaccessible cardinal κ and λ≥κ, and show that F^<SIA>_κλ-stationarity of a subset of {x∈P_κλ: x〓κ is a singular ordinal} is preserved in generic extensions by <κ-strategically closed partial ordering (Theorem 1). In particular, the sationarity of such a set is preserved in these generic extensions. We also give a proof of a theorem by T. Usuba which shows that F^<SIA>_κλ-stationarity in Theorem 1 cannot be replaced by stationarity (Theorem 3). This note complements [2] where Theorem 1 and Theorem 3 are cited without proof.
- 中部大学の論文
- 2005-12-15
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