کد مقاله کد نشریه سال انتشار مقاله انگلیسی ترجمه فارسی نسخه تمام متن
4661775 1344867 2016 24 صفحه PDF ندارد دانلود رایگان
عنوان انگلیسی مقاله
Model theoretic properties of the Urysohn sphere
ترجمه فارسی عنوان
خواص نظری مدل از حوزه Urysohn
کلمات کلیدی
حوزه Urysohn ؛ منطق پیوسته؛ نظریه طبقه بندی
03C45; 03B50; 03B60; 03C07Urysohn sphere; Continuous logic; Classification theory
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی

We characterize model theoretic properties of the Urysohn sphere as a metric structure in continuous logic. In particular, our first main result shows that the theory of the Urysohn sphere is SOPnSOPn for all n≥3n≥3, but does not have the fully finite strong order property. Our second main result is a geometric characterization of dividing independence in the theory of the Urysohn sphere. We further show that this characterization satisfies the extension axiom, and so forking and dividing are the same for complete types. Our results require continuous analogs of several tools and notions in classification theory. While many of these results are undoubtedly known to researchers in the field, they have not previously appeared in publication. Therefore, we include a full exposition of these results for general continuous theories.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 167, Issue 1, January 2016, Pages 49–72
نویسندگان
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