Speaker
Yong Cheng
Department of Philosophy, Wuhan University, Hubei Province, China
Talks at this conference:
Thursday, 17:50, J330 
On Rosser theories 
The notion of Rosser theories is introduced in [1]. Rosser theories play an important role in the study of the incompleteness phenomenon and metemathematics of arithmetic, and have important metemathematical properties. All definitions of Rosser theories in the literature are restricted to arithmetic languages which admit numerals for natural numbers. Results about Rosser theories in the literature are confined to 1ary relations. A general theory of Rosser theories for \(n\)ary relations for any \(n\geq 1\) and relationships among them is missing in the literature. We first introduce the notion of \(n\)Rosser theories, which generalizes the notion of Rosser theories for RE sets to \(n\)ary RE relations in a general setting via the notion of interpretation. Then, we introduce notions of exact \(n\)Rosser theories, effectively \(n\)Rosser theories and effectively exact \(n\)Rosser theories. Our definitions of these notions are not restricted to arithmetic languages admitting numerals for natural numbers. Then we systematically examine properties of these notions, and study relationships among these notions. Especially, we generalize some important theorems about Rosser theories for RE sets in the literature to \(n\)Rosser theories for any \(n\geq 1\). One important tool we use is the fact that for a disjoint pair of \(n\)ary RE relations, semi\(\sf DU\) implies \(\sf DU\). We give three different proofs of this fact. Let \(T\) be a consistent RE theory. We prove the following main theorems for any \(n\geq 1\):
Bibliography
