کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8904303 1633419 2018 38 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Topology and measure in logics for region-based theories of space
ترجمه فارسی عنوان
توپولوژی و اندازه گیری در منطق برای نظریه های منطقه مبتنی بر فضا
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی
The present paper explores the question of completeness of Lmincont and its extensions for individual topological spaces of interest: the real line, Cantor space, the rationals, and the infinite binary tree. A second aim is to study a different, algebraic model of logics for region-based theories of space, based on the Lebesgue measure algebra (or algebra of Borel subsets of the real line modulo sets of Lebesgue measure zero). As a model for point-free space, the algebra was first discussed in [2]. The main results of the paper are that Lmincont is weakly complete for any zero-dimensional, dense-in-itself metric space (including, e.g., Cantor space and the rationals); the extension Lmincont+(Con) is weakly complete for the real line and the Lebesgue measure contact algebra. We also prove that the logic Lmincont+(Univ) is weakly complete for the infinite binary tree.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 169, Issue 4, April 2018, Pages 277-311
نویسندگان
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