کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4661964 | 1633468 | 2014 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Introduction to clarithmetic III
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
منطق ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
The present paper constructs three new systems of clarithmetic (arithmetic based on computability logic): CLA8, CLA9 and CLA10. System CLA8 is shown to be sound and extensionally complete with respect to PA-provably recursive time computability. This is in the sense that an arithmetical problem A has a Ï-time solution for some PA-provably recursive function Ï iff A is represented by some theorem of CLA8. System CLA9 is shown to be sound and intensionally complete with respect to constructively PA-provable computability. This is in the sense that a sentence X is a theorem of CLA9 iff, for some particular machine M, PA proves that M computes (the problem represented by) X. And system CLA10 is shown to be sound and intensionally complete with respect to not-necessarily-constructively PA-provable computability. This means that a sentence X is a theorem of CLA10 iff PA proves that X is computable, even if PA does not “know” of any particular machine M that computes X.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 165, Issue 1, January 2014, Pages 241-252
Journal: Annals of Pure and Applied Logic - Volume 165, Issue 1, January 2014, Pages 241-252
نویسندگان
Giorgi Japaridze,