Beyond Erd\H{o}s-Kunen-Mauldin: Singular sets with shift-compactness properties

H. I. Miller; L. Miller-Van Wieren; A. J. Ostaszewski

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arXiv · 1901.09654

Beyond Erd\H{o}s-Kunen-Mauldin: Singular sets with shift-compactness properties

H. I. Miller·L. Miller-Van Wieren·A. J. Ostaszewski

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Abstract

The Kestelman-Borwein-Ditor Theorem asserts that a non-negligible subset of $\mathbb{R}$ which is Baire (=has the Baire property, BP) or measurable is shift-compact: it contains some subsequence of any null sequence to within translation by an element of the set. Effective proofs are recognized to yield (i) analogous category and Haar-measure metrizable generalizations for Baire groups and locally compact groups respectively, and (ii) permit under $V=L$ construction of co-analytic shift-compact subsets of R with singular properties, e.g. being concentrated on $\mathbb{Q}$, the rationals.

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BibTeX RIS

H. I. Miller, L. Miller-Van Wieren, A. J. Ostaszewski. 2019-01-28. Beyond Erd\H{o}s-Kunen-Mauldin: Singular sets with shift-compactness properties. https://arxiv.org/abs/1901.09654

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