Past exam of the mathematics course of the University of Cambridge / 2017 / iii / Paper 121 / 4 / i

A forcing atom is a condition $p\in \mathbb{P}$ such that any two strengthenings of $p$ are compatible forcing conditions:An atomless forcing order has no such condition; equivalently,The meaning of $q\perp r$ is that there is no common stronger condition. For an arbitrary partial order, an atom need not be a minimal element: the definition concerns compatibility below it. This distinction prevents a minimal-element definition from misclassifying an order with descending but mutually compatible conditions.