A framework for measuring the complexity of mathematical concepts

Using an untyped theory of sets and partial functions formulated in first-order free-logic with equality and a description operator, we develop a framework for the practical computation of the complexity of mathematical concepts. This includes an elementary theory of definitions and precise formulations of the notions of the definition tree and definition dag of a presentation of a mathematical concept. These combinatorial structures, which are essentially equivalent representations of the conceptual dependencies determined by the development of a given concept from primitive notions by purely logical definitions, provide the data for complexity computations.