Erdős Problem #1154
NOT DISPROVABLEdatabase updated 2026-01-24
Open in general, but there are models of set theory in which it is true — so it can't be disproved from the usual axioms (ZFC) alone.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Does there exist, for every \(\alpha \in [0, 1]\), a ring in \(\mathbb{R}\) with Hausdorff dimension \(\alpha\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 4 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/1154.Prizenone
Topicsanalysis
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1154
Attempts
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