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Transactions of the American Mathematical Society
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
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05458-4
PII: S 0002-9947(2012)05458-4
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.