کد مقاله کد نشریه سال انتشار مقاله انگلیسی ترجمه فارسی نسخه تمام متن
4661704 1344859 2016 34 صفحه PDF ندارد دانلود رایگان
عنوان انگلیسی مقاله
Tameness, uniqueness triples and amalgamation
ترجمه فارسی عنوان
ظرافت، سه گانه منحصر به فرد و ادغام
کلمات کلیدی
چکیده کلاس های ابتدایی؛ تمسخر؛ ادغام؛ رده بندی؛ فریم ها؛ سه گانه منحصر به فرد
03C45; 03C48; 03C52; 03C35Abstract elementary classes; Tameness; Amalgamation; Categoricity; Frames; Uniqueness triples
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی

We combine two approaches to the study of classification theory of AECs:(1)that of Shelah: studying non-forking frames without assuming the amalgamation property but assuming the existence of uniqueness triples and(2)that of Grossberg and VanDieren [6]: (studying non-splitting) assuming the amalgamation property and tameness.In [7] we derive a good non-forking λ+λ+-frame from a semi-good non-forking λ  -frame. But the classes Kλ+Kλ+ and ⪯↾Kλ+⪯↾Kλ+ are replaced: Kλ+Kλ+ is restricted to the saturated models and the partial order ⪯↾Kλ+⪯↾Kλ+ is restricted to the partial order ⪯λ+NF.Here, we avoid the restriction of the partial order ⪯↾Kλ+⪯↾Kλ+, assuming that every saturated model (in λ+λ+ over λ  ) is an amalgamation base and (λ,λ+)(λ,λ+)-tameness for non-forking types over saturated models (in addition to the hypotheses of [7]): Theorem 7.15 states that M⪯M+M⪯M+ if and only if M⪯λ+NFM+, provided that M   and M+M+ are saturated models.We present sufficient conditions for three good non-forking λ+λ+-frames: one relates to all the models of cardinality λ+λ+ and the two others relate to the saturated models only. By an ‘unproven claim’ of Shelah, if we can repeat this procedure ω   times, namely, ‘derive’ good non-forking λ+nλ+n frame for each n<ωn<ω then the categoricity conjecture holds.In [14], Vasey applies Theorem 7.8, proving the categoricity conjecture under the above ‘unproven claim’ of Shelah.In [10], we apply Theorem 7.15, proving the existence of primeness triples.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 167, Issue 2, February 2016, Pages 155–188
نویسندگان
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