paraconsistent set theory

Paraconsistent set theory is a mathematical framework that allows sets to contain contradictory information without collapsing into logical chaos. Unlike traditional set theory, where a contradiction (like a set both containing and not containing an element) invalidates the system, paraconsistent set theory accepts such contradictions but isolates their effects. This approach helps mathematicians explore concepts where inconsistency might naturally arise, such as in certain philosophical or computational contexts, while still maintaining meaningful, usable logical structures. Essentially, it broadens the boundaries of set theory to include and work with contradictions safely.