Open Problems in Mathematical Logic — Problem 31

Definitions and mathematical statement

The supplied record asks:

How about using dimension? (Define the above concepts by replacing measure by dimension.)

The intended task is to formulate dimensional analogues of previously introduced measure-based concepts. However, the referenced preceding concepts are absent from the supplied record. The underlying objects, the measure being replaced, the intended notion of dimension, and the properties or questions to be considered after replacement are unspecified. Consequently, no precise definitions or uniquely determined mathematical proposition, including its hypotheses and quantifiers, can be recovered from this record alone. The requested dimensional formulation remains unresolved pending the missing context.

Short English statement

The problem requests dimensional analogues of earlier measure-based concepts, but those concepts and the intended dimension are not supplied. A precise mathematical statement requires the preceding source context. The registry labels the problem open; this is a supplied status, not an independently verified assessment.

Sources

• Local UnsolvedMath registry, permanent ID $801019$, exact source problem code catalogue entry, titled Open Problems in Mathematical Logic --- Problem 31; collection: AMR Open Problem Lists. The record supplies the status open and attributes the proposal to Barmpalias, Gao et al., with proposed year 2026.
• Supplied source attribution: Barmpalias, Gao et al., Open Problems in Mathematical Logic (2026), Problem 31, https://arxiv.org/abs/2608.26628. The background records an access date of 2026-10-16 and extraction method arxiv_latex. These are supplied provenance details; the source and access claim have not been independently verified here.