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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On retraceable sets with rapid growth


Author: T. G. McLaughlin
Journal: Proc. Amer. Math. Soc. 40 (1973), 573-576
MSC: Primary 02F25
DOI: https://doi.org/10.1090/S0002-9939-1973-0340010-X
MathSciNet review: 0340010
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Abstract: We combine a refinement of a recent theorem of A. N. Degtev with a result of our own, in order to derive a general theorem about regressive sets which has the following

Corollary. If $ A$ is any point-decomposable $ \pi _1^0$ set then $ A$ has an infinite $ \pi _1^0$ subset $ B$ such that $ B$ has ``highly'' dense-simple complement and, moreover, all infinite $ \pi _1^0$ subsets of $ B$ are effectively decomposable in a strong sense (namely, they are all retraceable).


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DOI: https://doi.org/10.1090/S0002-9939-1973-0340010-X
Keywords: Retraceable set, regressive set, dense simplicity, pointdecomposability
Article copyright: © Copyright 1973 American Mathematical Society

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