کد مقاله کد نشریه سال انتشار مقاله انگلیسی ترجمه فارسی نسخه تمام متن
4661589 1344846 2016 22 صفحه PDF ندارد دانلود رایگان
عنوان انگلیسی مقاله
A generalization of the Łoś–Tarski preservation theorem
ترجمه فارسی عنوان
تعمیم قضیه حفظ لس ـ تارسکی
کلمات کلیدی
نظریه مدل؛ منطق مرتبه اول؛ قضیه حفظ لس ـ تارسکی
03C40; 03C52; 03C75; 03C13Model theory; First order logic; Łoś–Tarski preservation theorem
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی

We present new parameterized preservation properties that provide for each natural number k  , semantic characterizations of the ∃k∀⁎∃k∀⁎ and ∀k∃⁎∀k∃⁎ prefix classes of first order logic sentences, over the class of all structures and for arbitrary finite vocabularies. These properties, that we call preservation under substructures modulo k-cruxes and preservation under k-ary covered extensions respectively, correspond exactly to the classical properties of preservation under substructures and preservation under extensions, when k equals 0. As a consequence, we get a parameterized generalization of the Łoś–Tarski preservation theorem for sentences, in both its substructural and extensional forms. We call our characterizations collectively the generalized Łoś–Tarski theorem for sentences. We generalize this theorem to theories, by showing that theories that are preserved under k  -ary covered extensions are characterized by theories of ∀k∃⁎∀k∃⁎ sentences, and theories that are preserved under substructures modulo k  -cruxes, are equivalent, under a well-motivated model-theoretic hypothesis, to theories of ∃k∀⁎∃k∀⁎ sentences. In contrast to existing preservation properties in the literature that characterize the Σ20 and Π20 prefix classes of FO sentences, our preservation properties are combinatorial and finitary in nature, and stay non-trivial over finite structures as well.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 167, Issue 3, March 2016, Pages 189–210
نویسندگان
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