Double extension set theory

Summary

In mathematics, the Double extension set theory (DEST) is an axiomatic set theory proposed by Andrzej Kisielewicz consisting of two separate membership relations on the universe of sets, denoted here by $\in$ and $\varepsilon$, and a set of axioms relating the two. The intention behind defining the two membership relations is to avoid the usual paradoxes of set theory, without substantially weakening the axiom of unrestricted comprehension.