Material from Husserl's logic courses is used to piece together a picture of his theory of axiomatization and arithmetic that can be used to lay the groundwork for the study of its ramifications and implications for philosophy of logic and mathematics. It is argued that this shows that Husserl's theory is close to Hilbert's and belies claims of kinship with Brouwerian Intuitionism understood as the view that the collection of natural numbers and all of pure mathematics develops out of the self-unfolding of "the fundamental intellectual phenomenon of the falling apart of a moment of life into qualitatively different things, of which one is experienced as giving way to the other and yet is retained by an act of memory." It is contended that it needs to be determined whether Husserl's theory is a genuine, viable alternative to other, better known theories.