Effective categoricity of Abelian p-groups

2008/05/13 by Calvert, W., Cenzer, D., Harizanov, V. S. +1
#03C57 #03D45 #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)

paper · doi:10.48550/arxiv.0805.1889

Abstract

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 Δ⁰_α categorical if for any computable structure B isomorphic to A there is a Δ⁰_α function witnessing that the two are isomorphic. The present paper seeks to characterize Δ⁰_α categoricity for Abelian p-groups, and results of this kind are given for broad classes of Abelian p-groups and values of α. The remaining open cases are exhaustively described.

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