 For any set \(A\) and sentence \(p\) the remainder set \(A\bot p\) (“\(A\) remainder \(p\)”) is the set of inclusion-maximal subsets of \(A\) that do not imply \(p\). In other words, a set \(B\) is an element of \(A\bot p\) if and only if it it is a subset of \(A\) that does not imply \(p\), and there is no set \(B'\) not implying \(p\) such that \(B\subset B'\subseteq A\). The elements of \(A\bot p\) are called “remainders”.