Set theory and the nosology of hematological malignancies: Lymphomas are characterized by lymphoid differentiation, while leukemia definitions have no common property

The dividing line between leukemia and lymphoma is usually not very clear. We put forward the hypotheses that simple concepts of set theory are valuable tool in order to verify the consistency of the available definitions of leukemia and lymphoma. Set theory is the branch of mathematics that leads with collections or sets of objects and has many applications. A set can be described by listing the properties that its members must have in order to belong to the set. We developed a group of organizational properties regarding cellular origin (designated [O] for origin), progression [P] and differentiation [D] of the malignant hematopoietic cells. We selected definitions of leukemia and lymphoma from medical literature and analyzed these definitions according to properties [O], [P] and [D]. Fourteen definitions were selected for analysis (seven of leukemia and seven of lymphoma). For each definition, we listed the properties that define leukemia and lymphoma as a set of hematological malignancies. The main property that characterizes the set of lymphomas was the lymphoid differentiation. This property was present in all seven definitions of lymphoma and should be regarded a necessary condition to define this neoplasia. Definitions of leukemia were not uniform and no common property was present in all of them. Altogether, these results demonstrate that current definitions do not permit a precise classification of hematological malignancy as leukemia or lymphoma. The definitions of leukemia are not uniform and this term could be modified.