|کد مقاله||کد نشریه||سال انتشار||مقاله انگلیسی||ترجمه فارسی||نسخه تمام متن|
|4661702||1344859||2016||22 صفحه PDF||ندارد||دانلود کنید|
In this paper, we investigate Rosser-type Henkin sentences, namely, sentences asserting their own provability in the sense of Rosser, and local reflection principles based on Rosser provability predicates. First, we give a necessary and sufficient condition that a sentence is a Rosser-type Henkin sentence of some Rosser provability predicate, and prove that any negated Rosser sentence can be a Rosser-type Henkin sentence. Secondly, we prove the existence of a Rosser provability predicate whose Rosser-type Henkin sentences are all provable or refutable. Thirdly, we solve the question raised by Shavrukov, and give a Rosser provability predicate whose local reflection principle is strictly weaker than the usual one. At last, we investigate the hierarchy of partial local reflection principles based on Rosser provability predicates.
Journal: Annals of Pure and Applied Logic - Volume 167, Issue 2, February 2016, Pages 73–94