Main stages of development of the theory of functional subjective consumer behavior are defined by the analysis. The necessity mathematization axiomatic the theory are established analytically. It gives a detailed analysis of the axioms of classical and neoclassical theory of consumer behavior. Interpretation of the axioms is given in set-theoretic interpretation of the first-order predicate logic. Based on the mathematical Ernest Zermelo axiom of choice and rationality postulate choice carried out construction both axiom of choice independence and axiom of needs growth. It is made logical analysis considered axioms and is eliminated redundancy of the axioms. Attempts are made to build a system of axioms of the theory of functional subjective consumer behavior.