arXiv 0909.06662009-09math.LO

Borel reductions of profinite actions of SL(n,Z)

Samuel Coskey

发表信息：: Annals of pure and applied logic 161(10):1270-1279, 2010
DOI：: 10.1016/j.apal.2010.03.003

英文摘要：

Greg Hjorth and Simon Thomas proved that the classification problem for torsion-free abelian groups of finite rank \emph{strictly increases} in complexity with the rank. Subsequently, Thomas proved that the complexity of the classification problems for $p$-local torsion-free abelian groups of fixed rank $n$ are \emph{pairwise incomparable} as $p$ varies. We prove that if $3\leq m<n$ and $p,q$ are distinct primes, then the complexity of the classification problem for $p$-local torsion-free abelian groups of rank $m$ is again incomparable with that for $q$-local torsion-free abelian groups of rank $n$.

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