The complexity of maximal cofinitary groups

Kastermans, Bart

doi:10.1090/S0002-9939-08-09526-9

The complexity of maximal cofinitary groups
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Proc. Amer. Math. Soc. 137 (2009), 307-316 Request permission

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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