σ-Sets and σ-Antisets

In this paper we present a brief study of the \(\sigma\)-set-\(\sigma\)-antiset duality that occurs in \(\sigma\)-set theory and we also present the development of the integer space \(3^{A} = \left\langle 2^{A},2^{A^{-}} \right\rangle\) for the cardinals \({|A|} = {2,3}\) together with its algebraic properties. In this article, we also develop a presentation of some of the properties of fusion of \(\sigma\)-sets and finally we present the development and definition of a type of equations of one \(\sigma\)-set variable.