کد مقاله کد نشریه سال انتشار مقاله انگلیسی ترجمه فارسی نسخه تمام متن
4661595 1344846 2016 26 صفحه PDF ندارد دانلود رایگان
عنوان انگلیسی مقاله
Iterated elementary embeddings and the model theory of infinitary logic
ترجمه فارسی عنوان
تعبیه های ابتدایی مکرر و نظریه مدل منطق متناهی مبنا
کلمات کلیدی
خلاصه کلاس ابتدایی؛ انواع گالوا. تعبیه های ابتدایی مکرر ؛ مطلق
03C48; 03E15; 03E57; 03C45Abstract elementary classes; Galois types; Iterated elementary embeddings; Absoluteness
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی

We use iterations of elementary embeddings derived from countably complete ideals on ω1ω1 to provide a uniform proof of some classical results connecting the number of models of cardinality ℵ1ℵ1 in various infinitary logics to the number of syntactic types over the empty set. We introduce the notion of an analytically presented abstract elementary class (AEC), which allows the formulation and proof of generalizations of these results to refer to Galois types rather than syntactic types. We prove (Theorem 0.4) the equivalence of ℵ0ℵ0-presented classes and analytically presented classes and, using this, generalize (Theorem 0.5) Keisler's theorem on few models in ℵ1ℵ1 to bound the number of Galois types rather than the number of syntactic types. Theorem 0.6 gives a new proof (cf. [5]) for analytically presented AEC's of the absoluteness of ℵ1ℵ1-categoricity from amalgamation in ℵ0ℵ0 and almost Galois ω-stability.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 167, Issue 3, March 2016, Pages 309–334
نویسندگان
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