On existence in set theory. II: Relative productivity (Q2443122)

In this paper, the author investigates the strength of set existence of sentences with respect to a given class. This article continues his investigations in Part I [\textit{R. A. Freire}, Notre Dame J. Formal Logic 53, No. 4, 525--547 (2012; Zbl 1266.03054)]. He defines the relative degrees of existence requirements. Further, he introduces the concept of relative productivity and develops a technical approach to evaluate the relative degree of sentences of ZF. The author investigates the semilattice of simple relative degrees and obtains some results concerning this semilattice.