The complexity of maximal cofinitary groups

Author:
Bart Kastermans

Journal:
Proc. Amer. Math. Soc. **137** (2009), 307-316

MSC (2000):
Primary 03E47; Secondary 20Bxx

DOI:
https://doi.org/10.1090/S0002-9939-08-09526-9

Published electronically:
August 27, 2008

MathSciNet review:
2439455

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A cofinitary group is a subgroup of the infinite symmetric group in which each element of the subgroup has at most finitely many fixed points. A maximal cofinitary group is a cofinitary group that is maximal with respect to inclusion. We investigate the possible complexities of maximal cofinitary groups. In particular we show that (1) under the axiom of constructibility there exists a coanalytic maximal cofinitary group and (2) there does not exist an eventually bounded maximal cofinitary group. We also suggest some further directions for investigation.

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Additional Information

**Bart Kastermans**

Affiliation:
Department of Mathematics, University of Wisconsin, Madison, 480 Lincoln Drive, Madison, Wisconsin 53706

DOI:
https://doi.org/10.1090/S0002-9939-08-09526-9

Received by editor(s):
May 14, 2007

Received by editor(s) in revised form:
January 30, 2008

Published electronically:
August 27, 2008

Additional Notes:
The author was partially supported by Sun Yat-Sen University, Guangzhou, China

Communicated by:
Julia Knight

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.