On Classical Set-Compatibility

Abstract

In this paper, I generalise the logical concept of compatibility into a broader set-theoretical one. The basic idea is that two sets are incompatible if they produce at least one pair of opposite objects under some operation. I formalise opposition as an operation ′ ∶ E Ð→ E, where E is the set of opposable elements of our universe U, and I propose some models. From this, I define a relation C ∶ ℘U × ℘U × ℘U℘U, which has (mutual) logical compatibility as its more natural interpretation.