کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8904262 | 1633413 | 2018 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On constructivity and the Rosser property: a closer look at some Gödelean proofs
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
منطق ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
The proofs of Kleene, Chaitin and Boolos for Gödel's First Incompleteness Theorem are studied from the perspectives of constructivity and the Rosser property. A proof of the incompleteness theorem has the Rosser property when the independence of the true but unprovable sentence can be shown by assuming only the (simple) consistency of the theory. It is known that Gödel's own proof for his incompleteness theorem does not have the Rosser property, and we show that neither do Kleene's or Boolos' proofs. However, we show that a variant of Chaitin's proof can have the Rosser property. The proofs of Gödel, Rosser and Kleene are constructive in the sense that they explicitly construct, by algorithmic ways, the independent sentence(s) from the theory. We show that the proofs of Chaitin and Boolos are not constructive, and they prove only the mere existence of the independent sentences.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 169, Issue 10, October 2018, Pages 971-980
Journal: Annals of Pure and Applied Logic - Volume 169, Issue 10, October 2018, Pages 971-980
نویسندگان
Saeed Salehi, Payam Seraji,