A combinatorial problem and numerical semigroups

Let a = (a(1), ..., a(n)) and b = (b(1) ..., b(n)) be two n-tuples of positive integers, let X be a set of positive integers, and let g be a positive integer. In this work we show an algorithmic process in order to compute all the sets C of positive integers that fulfill the following conditions: 1. The cardinality of C is equal to g; 2. If x,y is an element of N{0} and x + y is an element of C, then C boolean AND{x,y} not equal empty set; 3. If x is an element of C and x-b(i)/a(i) is an element of N{0} for some i is an element of {1, ..., n}, then x-b(i)/a(i) is an element of C; 4. X boolean AND C = empty set.