Strictly Stratified Systems

Abstract

This paper is intended as a contribution to the formal theory of stratification systems. The paper has five sections. In Section 1, a method for analytically inducing an order over a multi-dimensional status is discussed. It is believed that such a technique can aid in the specification of conceptual tasks within stratification theory, as well as serve as a baseline in actual measurements. It is subsequently employed in the axiomatic work of Sections 3 and 4. In Section 2, there is a brief discussion of the axiomatic method as a prelude to the system developed in the following two sections. In Section 3, the axioms are stated. In Section 4, various elementary consequences of the axioms are shown; most importantly, various concepts which are intuitively important in stratification theory are shown to be definable (e.g., a class system with a determinate number of classes). Finally, in Section 5, there is a concluding discussion of the picture of stratification which emerges within this work.