کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4595722 1336131 2017 24 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Modules over quantaloids: Applications to the isomorphism problem in algebraic logic and π-institutions
ترجمه فارسی عنوان
ماژول های بیش از quantaloid: برنامه های کاربردی برای مسئله ایزومورفیسم در منطق جبری و π-institutions
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

We solve the isomorphism problem in the context of abstract algebraic logic and of π-institutions, namely the problem of when the notions of syntactic and semantic equivalence among logics coincide. The problem is solved in the general setting of categories of modules over quantaloids. We introduce closure operators on modules over quantaloids and their associated morphisms. We show that, up to isomorphism, epis are morphisms associated with closure operators. The notions of (semi-)interpretability and (semi-)representability are introduced and studied. We introduce cyclic modules, and provide a characterization for cyclic projective modules as those having a g-variable. Finally, we explain how every π-institution induces a module over a quantaloid, and thus the theory of modules over quantaloids can be considered as an abstraction of the theory of π-institutions.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 221, Issue 1, January 2017, Pages 1–24
نویسندگان
, ,