An alternative set theory in which every element can have an anti-element, giving rise to sigma-sets and their sigma-antisets. The sigma-antiset of a set is its inverse under a fusion operator: fusing a set with its antiset annihilates matching element/anti-element pairs and returns the empty set. Covers the fusion operator (built from a star-intersection and star-difference, commutative but non-associative), the resulting sigma-set/sigma-antiset duality, an associated integer space construction, and equations in one sigma-set variable.
This paper develops sigma-set theory, an alternative set theory in which elements may possess anti-elements. It defines the sigma-antiset A-minus of a sigma-set A as its fusion inverse: fusing a sigm…