On Definable J-­sets

Studies in Logic, Vol. 19, No. 3 (2026): 49–58                                  PII: 1674-3202(2026)-03-0049-10

Zhentao Zhang

Abstract. We study definable J­-sets for definable groups and compare them with weakly generic sets. We show that J­-property, the property that J­-sets coincide with weakly generic sets, is invariant on enough saturated models, and hence a model­theoretical property. We have a positive result for superstable commutative groups. We also give an example without J-­property.