English

On definable J-sets

Logic 2025-04-29 v3

Abstract

We study definable J-sets for definable groups and compare them with weakly generic sets. We show that the property that J-sets coincide with weakly generic sets is invariant on enough saturated models, and hence a model-theoretical property. We have positive results for superstable commutative groups and some easy examples in pCF. We also give an example for noncoincidence.

Keywords

Cite

@article{arxiv.2502.05733,
  title  = {On definable J-sets},
  author = {Zhentao Zhang},
  journal= {arXiv preprint arXiv:2502.05733},
  year   = {2025}
}
R2 v1 2026-06-28T21:37:30.782Z