Some Solved and Unsolved Remainder Equations

Abstract The remainder set A ⟂ B of a set of sentences A modulo a set of sentences B is the set of all maximal subsets of A not implying any element of B. A remainder equation is an expression containing remainder sets, such as { A } = B ⟂ X , in which at least one set is unknown. Solutions to some classes of remainder equations are reported, and some unsolved problems are listed.