It is proved that the number of numerical semigroups with a fixed number n of star operations is finite if n > 1. The result is then extended to the class of analytically irreducible residually rational one-dimensional Noetherian rings with finite residue field and integral closure equal to a fixed discrete valuation domain.
Spirito, D. (2015). Star operations on numerical semigroups. COMMUNICATIONS IN ALGEBRA, 43(7), 2943-2963 [10.1080/00927872.2014.908201].