|کد مقاله||کد نشریه||سال انتشار||مقاله انگلیسی||ترجمه فارسی||نسخه تمام متن|
|4661595||1344846||2016||26 صفحه PDF||ندارد||دانلود کنید|
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. ) for analytically presented AEC's of the absoluteness of ℵ1ℵ1-categoricity from amalgamation in ℵ0ℵ0 and almost Galois ω-stability.
Journal: Annals of Pure and Applied Logic - Volume 167, Issue 3, March 2016, Pages 309–334