کد مقاله کد نشریه سال انتشار مقاله انگلیسی ترجمه فارسی نسخه تمام متن
4661710 1344860 2015 12 صفحه PDF ندارد دانلود رایگان
عنوان انگلیسی مقاله
Nonstandardness and the bounded functional interpretation
ترجمه فارسی عنوان
تفسیر کاربردی محدود و غیراستاندارد
کلمات کلیدی
تفسیرهای کاربردی؛ حساب غیراستاندارد؛ Majorizability؛ تفسیر کاربردی محدود
Functional interpretations; Nonstandard arithmetic; Majorizability; Bounded functional interpretation
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی

The bounded functional interpretation of arithmetic in all finite types is able to interpret principles like weak König's lemma without the need of any form of bar recursion. This interpretation requires the use of intensional (rule-governed) majorizability relations. This is a somewhat unusual feature. The main purpose of this paper is to show that if the base domain of the natural numbers is extended with nonstandard elements, then the bounded functional interpretation can be seen as falling out from a functional interpretation of nonstandard number theory without intensional notions. The original bounded functional interpretation can be seen as the trace left behind by the new interpretation when one sees it restricted to the standard number theoretical setting.We also answer an open question regarding the conservativity of the transfer principle vis-à-vis functional interpretations of nonstandard arithmetic.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 166, Issue 6, June 2015, Pages 701–712
نویسندگان
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