DIMENSION AND MEASURE IN PSEUDOFINITE <i>H</i>-STRUCTURES
Abstract We study H -structures associated with $SU$ -rank 1 measurable structures. We prove that the $SU$ -rank of the expansion is continuous and that it is uniformly definable in terms of the parameters of the formulas. We also introduce notions of dimension and measure for definable sets in the expansion and prove they are uniformly definable in terms of the parameters of the formulas.
Authors
- Tingxiang Zou (ORCID: https://orcid.org/0000-0003-4370-8765)
- Darío García (ORCID: https://orcid.org/0000-0002-5141-7346)
- Alexander Berenstein (ORCID: https://orcid.org/0000-0002-1469-1864)
Institutions
- Université Claude Bernard Lyon 1 (FR)
- Universidad de Los Andes (BO)
Publication Details
- Journal
- Journal of Symbolic Logic
- Published
- 2025-03-01
- DOI
- https://doi.org/10.1017/jsl.2023.75
- Primary Topic
- Advanced Topology and Set Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00