کد مقاله کد نشریه سال انتشار مقاله انگلیسی ترجمه فارسی نسخه تمام متن
4661590 1344846 2016 24 صفحه PDF ندارد دانلود رایگان
عنوان انگلیسی مقاله
Transductions in arithmetic
ترجمه فارسی عنوان
ترارسانی در علم حساب
کلمات کلیدی
ترارسانی ؛ اثبات پذیری منطق؛ قضیه ناتمامیت دوم
03B25; 03F25; 03F30; 03F45Interpretability; Provability Logic; Second Incompleteness Theorem
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی

In this paper we study a new relation between sentences: transducibility. The idea of transducibility is based on an analysis of Feferman's Theorem that the inconsistency of a theory U is interpretable over U. Transducibility is based on a converse of Feferman's Theorem: if a sentence is interpretable over a theory U, it is, in a sense that we will explain, an inconsistency statement for U over U.We show that, for a wide class of theories U, transducibility coincides with interpretability over U   and, for an even wider class, it coincides with Π1Π1-conservativity over U  . Thus, transducibility provides a new way of looking at interpretability and Π1Π1-conservativity. On the other hand, we will show that transducibility admits variations that are distinct from interpretability and Π1Π1-conservativity.We show that transducibility satisfies the interpretability logic ILM.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 167, Issue 3, March 2016, Pages 211–234
نویسندگان
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