Computer Science > Logic in Computer Science
[Submitted on 22 Sep 2021 (v1), last revised 21 Sep 2023 (this version, v4)]
Title:The Point-to-Set Principle and the Dimensions of Hamel Bases
View PDFAbstract:We prove that every real number in [0,1] is the Hausdorff dimension of a Hamel basis of the vector space of reals over the field of rationals.
The logic of our proof is of particular interest. The statement of our theorem is classical; it does not involve the theory of computing. However, our proof makes essential use of algorithmic fractal dimension--a computability-theoretic construct--and the point-to-set principle of J. Lutz and N. Lutz (2018).
Submission history
From: Jack Lutz [view email][v1] Wed, 22 Sep 2021 18:51:45 UTC (9 KB)
[v2] Tue, 28 Sep 2021 12:06:15 UTC (67 KB)
[v3] Wed, 20 Sep 2023 03:07:06 UTC (74 KB)
[v4] Thu, 21 Sep 2023 21:04:12 UTC (74 KB)
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