Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



Describing free groups, Part II: $ \Pi^0_4$ hardness and no $ \Sigma_{2}^{0}$ basis

Authors: Charles McCoy and John Wallbaum
Journal: Trans. Amer. Math. Soc. 364 (2012), 5729-5734
MSC (2010): Primary 03C57
Published electronically: June 21, 2012
MathSciNet review: 2946929
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We continue the study of free groups from a computability theoretic perspective. In particular, we show that for $ F_{\infty }$, the free group on a countable number of generators, the descriptions given in our preceding paper are the best possible.

References [Enhancements On Off] (What's this?)

  • 1. M. Bestvina and M. Feighn, ``Definable and negligible subsets of free groups'', in process.
  • 2. J. Carson, V. Harizanov, J. Knight, K. Lange, C. McCoy, A. Morozov, S. Quinn, C. Safranski, J. Wallbaum, ``Describing free groups'', Tran. Amer. Math. Soc., this issue.
  • 3. B. Fine, G. Rosenberger, D. Spellman, M. Stille, ``Test Words, Generic Elements and Almost Primitivity'', Pacific Journal of Mathematics, Vol. 190, no. 2 (1999), pp. 277-297. MR 1722895 (2000j:20035)
  • 4. A. Karass and D. Solitar, ``On Finitely Generated Subgroups of a Free Group'', Proceedings of the American Mathematical Society, vol. 22, no. 1 (July 1969), pp. 209-213. MR 0245655 (39:6961)
  • 5. M. Takahasi, ``Note on locally free groups'', J. Inst Polytech. Osaka City Univ. Ser. A. Math, 1 (1950), pp. 65-70. MR 0041845 (13:9h)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 03C57

Retrieve articles in all journals with MSC (2010): 03C57

Additional Information

Charles McCoy
Affiliation: Deparment of Mathematics, University of Portland, Portland, Oregon 97203

John Wallbaum
Affiliation: Deparment of Mathematical Sciences, Eastern Mennonite University, Harrisonburg, Virginia 22802

Received by editor(s): August 25, 2010
Published electronically: June 21, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society