  In this paper we develop a theory called $\sigma$-Set Theory, in which we
present an axiom system developed from the study of Set Theories of
Zermelo-Fraenkel, Neumann-Bernays-Godel and Morse-Kelley. In $\sigma$-Set
Theory, we present the proper existence of objects called $\sigma$-antielement,
$\sigma$-antiset, natural numbers, antinatural numbers and generated
$\sigma$-set by two $\sigma$-sets, from which we obtain, among other things, a
commutative non-associative algebraic structure called Integer Space $3^{X}$,
which corresponds to the algebraic completion of $2^{X}$.
