THE CLASSIFICATION PROBLEM FOR p-LOCAL TORSION-FREE ABELIAN GROUPS OF RANK TWO-Reference-Cited by-同舟云学术

THE CLASSIFICATION PROBLEM FOR p-LOCAL TORSION-FREE ABELIAN GROUPS OF RANK TWO

Published:2006-12 Issue:02 Volume:06 Page:233-251
ISSN:0219-0613
Container-title:Journal of Mathematical Logic
language:en
Short-container-title:J. Math. Log.

Author:

HJORTH GREG¹,THOMAS SIMON²

Affiliation:

1. Mathematics Department, UCLA, Los Angeles, CA 90095, USA

2. Mathematics Department, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA

Abstract

We prove that if p ≠ q are distinct primes, then the classification problems for p-local and q-local torsion-free abelian groups of rank two are incomparable with respect to Borel reducibility.

Publisher

World Scientific Pub Co Pte Lt

Subject

Logic

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021906130600058X

Reference17 articles.

1. Linear algebraic groups and countable Borel equivalence relations

2. Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces

3. Around nonclassifiability for countable torsion free abelian groups

4. Borel equivalence relations and classifications of countable models

5. Memoirs of American Mathematical Society No. 833;Hjorth G.,2005

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The definable content of homological invariants I: Ext$\mathrm{Ext}$ and lim1$\mathrm{lim}^1$;Proceedings of the London Mathematical Society;2024-08-27

2. Orbit equivalence and Borel reducibility rigidity for profinite actions with spectral gap;Journal of the European Mathematical Society;2016

3. Classes of Ulm type and coding rank-homogeneous trees in other structures;The Journal of Symbolic Logic;2011-09

4. The classification of torsion-free abelian groups of finite rank up to isomorphism and up to quasi-isomorphism;Transactions of the American Mathematical Society;2011-08-31

5. Embedding solenoids in foliations;Topology and its Applications;2011-07