 Interpreted as such, Dedekind’s approach is related to that of the “American Postulate Theorists”,  E. Huntington, O. Veblen, etc. (cf. Awodey &amp; Reck 2002). There is also a close connection to, and a clear influence on, the formal axiomatics developed by Hilbert and Bernays later (cf. Sieg 2010, 2014, also Hallett 1994, 1995, 2003). For all of these thinkers, what is crucial in, and sufficient for, mathematics is that the completeness and consistency of certain basic concepts, or of the corresponding systems of axioms, are established. In Dedekind’s case, completeness is to be understood in a semantic sense, as based on categoricity; likewise, consistency is to be understood semantically, as satisfiability (Dedekind 1890); and both are tied to his distinctive combination of logicism and structuralism.