Effective categoricity of Abelian p-groups

Autor:	Calvert, W., Cenzer, D., Harizanov, V. S., Morozov, A.
Rok vydání:	2008
Předmět:	Mathematics - Logic Mathematics - Group Theory 03D45 03C57
Druh dokumentu:	Working Paper
Popis:	Let p be a fixed prime. An Abelian p-group is an Abelian group (not necessarily finitely generated) in which every element has for its order some power of p. The countable Abelian p-groups are classified by Ulm's theorem, and Khisamiev characterized the Abelian p-groups with computable copies. A computable structure A is said to be $\Delta^0_\alpha$ categorical if for any computable structure B isomorphic to A there is a $\Delta^0_\alpha$ function witnessing that the two are isomorphic. The present paper seeks to characterize $\Delta^0_\alpha$ categoricity for Abelian p-groups, and results of this kind are given for broad classes of Abelian p-groups and values of $\alpha$. The remaining open cases are exhaustively described. Comment: Improved version accepted for publication in Annals of Pure and Applied Logic
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0805.1889 Zobrazit plný text záznamu View this record from Arxiv