Non-wellfounded mereology

In philosophy, specifically metaphysics, mereology is the study of parthood relationships. In mathematics and formal logic, wellfoundedness prohibits ${\displaystyle \cdots <x<\cdots <x<\cdots }$ for any x.

Thus non-wellfounded mereology treats topologically circular, cyclical, repetitive, or other eventual self-containment.

More formally, non-wellfounded partial orders may exhibit ${\displaystyle \cdots <x<\cdots <x<\cdots }$ for some x whereas well-founded orders prohibit that.