کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6424774 1633472 2013 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Applications of pcf for mild large cardinals to elementary embeddings
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
پیش نمایش صفحه اول مقاله
Applications of pcf for mild large cardinals to elementary embeddings
چکیده انگلیسی

The following pcf results are proved:1. Assume that κ>ℵ0is a weakly compact cardinal. Let μ>2κbe a singular cardinal of cofinality κ. Then for every regular λsup{suppcfσ⁎-complete(a)|a⊆Reg∩(μ+,χ)and|a|<μ}.As an application we show that:if κ is a measurable cardinal and j:V→Mis the elementary embedding by a κ-complete ultrafilter over κ, then for every τ the following holds:1.if j(τ)is a cardinal then j(τ)=τ;2.|j(τ)|=|j(j(τ))|;3.for any κ-complete ultrafilter W on κ, |j(τ)|=|jW(τ)|. The first two items provide affirmative answers to questions from Gitik and Shelah (1993) [2] and the third to a question of D. Fremlin.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 164, Issue 9, September 2013, Pages 855-865
نویسندگان
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