We present a formal first-order theory of artificial objects, i.e., objects made out of a finite number of parts and subject to assembling and dismantling processes. These processes are absolutely reversible. The theory is an extension of the theory of finite sets with urelements. The notions of transformation and identity are defined and studied on the assumption that the objects are homogeneous, that is to say, all their atomic parts are of equal ontological importance. Particular emphasis is given to the (...) behavior of classes of artifacts in time. We call such classes satisfying certain preservation conditions worlds. Various results concerning the existence, extension, and completeness of worlds are proved. (shrink)