摘要：In this talk, I will present a recursion-theoretic view of Levi's theorem: an abelian group is torsion-free if and only if it orderable. Downey and Kurtz first considered the effective version of Levi's theorem, and proved the existence of a computabletorsion-free abelian group which cannot be effectively orderable. Simpson and his student later proved that in terms of reverse mathematics, Levi's theorem has strength the same as WKL0 (Weak Konig Lemma). Kach, Lange and Solomon(APAL 2013) consider the degree-version of Levi's theorem and showed the existence of a c.e. set C and computable torsion-free abelian group G with infinite rank, admitting exactly two computable orderings such that every C-computable order on G is computable.In this paper, Kach, et al. pointed out that there are infinitely many such Cs, and these Cs can have low degree. Martin shows in his PhD thesis (U. Conn) that C can be of high degree. Our main result provides a close relation between such Cs and PA degrees,and shows that such Cs can be any incomplete c.e. set.

It is a joint work with Frank Stephan (NUS) and Huishan Wu (BLCU).

报告人：吴国华 教授 新加坡南洋理工大学

报告时间：2018年11月30日14:30-15:30

报告地点：瘦西湖校区38号楼103室

主办单位：扬州大学数学科学学院

欢迎广大师生参加！