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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On retraceable sets with rapid growth
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by T. G. McLaughlin PDF
Proc. Amer. Math. Soc. 40 (1973), 573-576 Request permission

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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Additional Information
  • © Copyright 1973 American Mathematical Society
  • 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