کد مقاله کد نشریه سال انتشار مقاله انگلیسی ترجمه فارسی نسخه تمام متن
4661581 1344845 2016 64 صفحه PDF ندارد دانلود رایگان
عنوان انگلیسی مقاله
Building independence relations in abstract elementary classes
ترجمه فارسی عنوان
ایجاد روابط استقلال در کلاس های ابتدایی انتزاعی
کلمات کلیدی
کلاس ابتدایی خلاصه ؛ انشعاب؛ فریم خوب
primary, 03C48; secondary, 03C45, 03C52, 03C55Abstract elementary classes; Forking; Good frames; Categoricity; Superstability; Tameness
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی

We study general methods to build forking-like notions in the framework of tame abstract elementary classes (AECs) with amalgamation. We show that whenever such classes are categorical in a high-enough cardinal, they admit a good frame: a forking-like notion for types of singleton elements. Theorem 0.1 Superstability from categoricity. Let K be a  (<κ)(<κ)-tame AEC with amalgamation. If  κ=ℶκ>LS(K)κ=ℶκ>LS(K)and K is categorical in a  λ>κλ>κ, then:
• K is stable in any cardinal μ with  μ≥κμ≥κ.
• K is categorical in κ.
• There is a type-full good λ-frame with underlying class  KλKλ.Under more locality conditions, we prove that the frame extends to a global independence notion (for types of arbitrary length). Theorem 0.2 A global independence notion from categoricity. Let K be a densely type-local, fully tame and type short AEC with amalgamation. If K is categorical in unboundedly many cardinals, then there exists  λ≥LS(K)λ≥LS(K)such that  K≥λK≥λadmits a global independence relation with the properties of forking in a superstable first-order theory.As an application, we deduce (modulo an unproven claim of Shelah) that Shelah's eventual categoricity conjecture for AECs (without assuming categoricity in a successor cardinal) follows from the weak generalized continuum hypothesis and a large cardinal axiom. Corollary 0.3. Assume  2λ<2λ+2λ<2λ+for all cardinals λ, as well as an unpublished claim of Shelah. If there exists a proper class of strongly compact cardinals, then any AEC categorical in some high-enough cardinal is categorical in all high-enough cardinals.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 167, Issue 11, November 2016, Pages 1029–1092
نویسندگان
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