The term "cumulative hierarchy" refers to the hierarchical organization of sets in mathematical logic. Other synonyms for this term include "set-theoretical hierarchy", "hierarchical universe of sets", or simply "hierarchy of sets". The cumulative hierarchy is a fundamental concept in the study of set theory and plays a vital role in many areas in mathematics such as topology, analysis, and algebra. Other related terms that are often used in conjunction with the cumulative hierarchy include "ordinal number", "cardinal number", and "transfinite induction". The various synonyms for the cumulative hierarchy are useful in describing the complex and intricate structure of sets in mathematics, and they help to make the subject more accessible to readers and researchers alike.