In this paper, we shall show that an unlimited number of additive single faults can be isolated under mild conditions if a general isolation scheme is applied. Multiple faults are also covered. The approach is algebraic and is based on a set representation of faults, where all faults within a set can occur simultaneously, whereas faults belonging to different fault sets appear disjoint in time. The proposed fault detection and isolation (FDI) scheme consists of three steps. A fault detection (FD) step is followed by a fault set isolation (FSI) step. Here the fault set is isolated wherein the faults have occurred. The last step is a fault isolation (FI) of the faults occurring in a specific fault set, i.e. equivalent with the standard FI step. A simple example demonstrates how to turn the algebraic necessary and sufficient conditions into explicit algorithms for designing filter banks, which implement isolability.