کد مقاله کد نشریه سال انتشار مقاله انگلیسی ترجمه فارسی نسخه تمام متن
4661620 1344849 2016 23 صفحه PDF ندارد دانلود رایگان
عنوان انگلیسی مقاله
Expansions of o-minimal structures by dense independent sets
ترجمه فارسی عنوان
گسترش ساختارهای o حداقل مجموعه مستقل متراکم
کلمات کلیدی
حداقل O ؛ گروه متراکم سفارش؛ محمول؛ هسته باز؛ از بین بردن تصورات
primary, 03C64; secondary, 06F20, 03C10, 20F60o-Minimal; Densely ordered group; Independent predicate; Open core; Eliminate imaginaries
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی

Let MM be an o-minimal expansion of a densely ordered group and HH be a pairwise disjoint collection of dense subsets of M   such that ⋃H⋃H is definably independent in MM. We study the structure (M,(H)H∈H)(M,(H)H∈H). Positive results include that every open set definable in (M,(H)H∈H)(M,(H)H∈H) is definable in MM, the structure induced in (M,(H)H∈H)(M,(H)H∈H) on any H0∈HH0∈H is as simple as possible (in a sense that is made precise), and the theory of (M,(H)H∈H)(M,(H)H∈H) eliminates imaginaries and is strongly dependent and axiomatized over the theory of MM in the most obvious way. Negative results include that (M,(H)H∈H)(M,(H)H∈H) does not have definable Skolem functions and is neither atomic nor satisfies the exchange property. We also characterize (model-theoretic) algebraic closure and thorn forking in such structures. Throughout, we compare and contrast our results with the theory of dense pairs of o-minimal structures.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 167, Issue 8, August 2016, Pages 684–706
نویسندگان
, , ,