کد مقاله کد نشریه سال انتشار مقاله انگلیسی ترجمه فارسی نسخه تمام متن
4661564 1344843 2016 16 صفحه PDF ندارد دانلود رایگان
عنوان انگلیسی مقاله
Limit spaces with approximations
ترجمه فارسی عنوان
فضاهای محدود با تقریب
کلمات کلیدی
نظریه محاسبات در انواع بالاتر؛ ریاضیات و سازنده؛ قضیه چگالی؛ فضاهای محدود
03D75; 03D80; 03F60; 03F65Computability theory at higher types; Constructive mathematics; Density theorem; Limit spaces
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی

Abstracting from a presentation of the density theorem for the hierarchy Ct(ρ)Ct(ρ) of countable functionals over NN given by Normann in [12], we define two subcategories of limit spaces, the limit spaces with approximations, and the limit spaces with general approximations, for both of which a density theorem holds directly. We show that these categories are cartesian closed, and we give examples of such limit spaces and of density theorems for hierarchies of functionals over them. Most of our main proofs are within Bishop's informal system of constructive mathematics BISH. In a limit space with (general) approximations the approximation functions are given beforehand as an internal part of the structure under study. In this way limit spaces with (general) approximations form a constructive approach to abstract limit spaces, reflecting at the same time the central idea of Normann's Program of Internal Computability.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 167, Issue 9, September 2016, Pages 737–752
نویسندگان
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