کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4662295 1633514 2009 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Interpretability in
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
پیش نمایش صفحه اول مقاله
Interpretability in
چکیده انگلیسی

In this paper, we study (), the interpretability logic of . As is neither an essentially reflexive theory nor finitely axiomatizable, the two known arithmetical completeness results do not apply to : () is not or . () does, of course, contain all the principles known to be part of (All), the interpretability logic of the principles common to all reasonable arithmetical theories. In this paper, we take two arithmetical properties of and see what their consequences in the modal logic () are. These properties are reflected in the so-called Beklemishev Principle , and Zambella’s Principle , neither of which is a part of (All). Both principles and their interrelation are submitted to a modal study. In particular, we prove a frame condition for . Moreover, we prove that follows from a restricted form of . Finally, we give an overview of the known relationships of () to important other interpretability principles.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 161, Issue 2, November 2009, Pages 128-138