Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 30 min ago
PreprintarXiv licencearXiv

A Zero--One Law for Subrings of the Reals Closed under Binary Interleaving

  • Yi Wang
Open at sourcePDFDOICite

Abstract

Erdős Problem 1154 asks whether every number in [0,1] occurs as the Hausdorff dimension of a subring or subfield of ℝ. We prove that a subring of ℝ closed under binary interleaving has Hausdorff dimension either zero or one. Consequently, every Turing ideal and its associated subfield satisfy the same dichotomy.

Related

  1. Combinatorics of translations of meager and closed measure zero sets
    Aleksander Cieślak
    arXivPreprintCC BY 4.0Full textLogic & foundationsarXiv
  2. Equilibrium Laws for Julia's Zero and the Hyperbolic Zero of Binary Forms
    Artur Elezi
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  3. Zero-sets and closed sets with countable closure index
    Jonás Martínez
    Applied General TopologyPeer-reviewedCC BY-NC-NDFull textGeometry & topologyDOAJ
  4. Lie dimension subrings
    Laurent Bartholdi, Inder Bir S. Passi
    Internat. J. Algebra Comput.Peer-reviewedLicence not statedFull text2 citedAlgebra & number theoryHAL
  5. Equivariant Homotopy Interleaving and Persistent Whitehead Theorem
    Kushal Halder, Subhankar Sau, Debasis Sen
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{wang2026zeroone,
  title = {{A Zero--One Law for Subrings of the Reals Closed under Binary Interleaving}},
  author = {Yi Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.18955},
  eprint = {2608.18955},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.18955},
}
RIS
TY  - UNPB
TI  - A Zero--One Law for Subrings of the Reals Closed under Binary Interleaving
AU  - Yi Wang
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2608.18955
UR  - https://arxiv.org/abs/2608.18955
AB  - Erdős Problem 1154 asks whether every number in [0,1] occurs as the Hausdorff dimension of a subring or subfield of ℝ. We prove that a subring of ℝ closed under binary interleaving has Hausdorff dimension either zero or one. Consequently, every Turing ideal and its associated subfield satisfy the same dichotomy.
ER  -