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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Finding bases of uncountable free abelian groups is usually difficult
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by Noam Greenberg, Dan Turetsky and Linda Brown Westrick PDF
Trans. Amer. Math. Soc. 370 (2018), 4483-4508 Request permission

Abstract:

We investigate effective properties of uncountable free abelian groups. We show that identifying free abelian groups and constructing bases for such groups is often computationally hard, depending on the cardinality. For example, we show, under the assumption $V=L$, that there is a first-order definable free abelian group with no first-order definable basis.
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Additional Information
  • Noam Greenberg
  • Affiliation: School of Mathematics and Statistics, Victoria University of Wellington, Wellington, New Zealand
  • MR Author ID: 757288
  • ORCID: 0000-0003-2917-3848
  • Email: greenberg@msor.vuw.ac.nz
  • Dan Turetsky
  • Affiliation: School of Mathematics and Statistics, Victoria University of Wellington, Wellington, New Zealand
  • MR Author ID: 894314
  • Email: dan.turetsky@vuw.ac.nz
  • Linda Brown Westrick
  • Affiliation: School of Mathematics and Statistics, Victoria University of Wellington, Wellington, New Zealand
  • Address at time of publication: Department of Mathematics, University of Connecticut, 341 Mansfield Road U1009, Storrs, Connecticut 06269-1009
  • Email: westrick@uconn.edu
  • Received by editor(s): January 23, 2016
  • Received by editor(s) in revised form: March 7, 2017
  • Published electronically: December 14, 2017
  • Additional Notes: The first author was supported by the Marsden Fund, a Rutherford Discovery Fellowship from the Royal Society of New Zealand, and by the Templeton Foundation via the Turing centenary project “Mind, Mechanism and Mathematics”.
    The third author was supported by the Rutherford Discovery Fellowship as a postdoctoral fellow.
  • © Copyright 2017 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 4483-4508
  • MSC (2010): Primary 03C57; Secondary 03D60
  • DOI: https://doi.org/10.1090/tran/7232
  • MathSciNet review: 3811535