Modern Set

TL;DR

This paper proposes a generalized set theory that relaxes classical properties like the law of excluded middle and distributive laws, aiming to explore more flexible foundational frameworks.

Contribution

It introduces a novel generalized set theory that removes traditional logical constraints from classical set theory.

Findings

The generalized set theory broadens the scope of set concepts.

It challenges classical logical laws within set theory.

Potential applications in non-classical logic systems.

Abstract

In this paper, we intend to generalize the classical set theory as much as possible. we will do this by freeing sets from the regular properties of classical sets; e.g., the law of excluded middle, the law of non-contradiction, the distributive law, the commutative law,etc....