An Axiomatic Method Applied to the Theory of Urban Evolution

The goal of this paper is to lay out a clear and specific mathematical method for solving problems and then to apply that method to the Theory of Urban Evolution within the field of Urban Economics. The application of the method will focus specifically on how mathematicians develop axioms to unify a field where independent statements exist; that is, statements that are unaccounted for by the field’s current axioms. This will be developed as a special case of the General Axiomatic Method by analyzing historical axiomization of fields in mathematics. After the Axiomatic Method has been developed, the Foundations of Urban Economics will be analyzed to determine the whether or not the Axiomatic Method is necessary. Following this, the Theory of Urban Evolution will be discussed to as a potential independent statement that could be unified with the Foundations of Urban Economics. Finally, the Axiomatic Method will be applied in an attempt to unify the Theory of Urban Evolution with the Foundations of Urban Economics so that we may achieve a new way of understanding how urban regions act as evolutionary ecosystems.