Dimension and measure in pseudofinite H-structures
Alexander Berentein, Dario Garcia, Tingxiang Zou
TL;DR
This paper investigates the properties of H-structures related to SU-rank 1 measurable structures, establishing continuity and uniform definability of rank, dimension, and measure in the expansion.
Contribution
It introduces and proves the uniform definability of dimension and measure for definable sets in H-structures associated with SU-rank 1 measurable structures.
Findings
SU-rank of the expansion is continuous
Dimension and measure are uniformly definable
Results apply to definable sets in the expansion
Abstract
We study H-structures associated to 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.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology · Rings, Modules, and Algebras