Most of Finkelstein's work is directed toward a quantum theory of space-time structure. He early on accepted the conclusion of John von Neumann that anomalies of quantum mechanical measurement are anomalies of the logic of quantum mechanical systems. Therefore, he formed quantum analogues of set theory, the standard language for classical space-time structures, and proposed that space-time is a quantum set of space-time quanta dubbed "chronons", a form of quantum computer with spins for quantum bits, as a quantum version of the cellular automaton of von Neumann. His early quantum space-times proving unphysical, he later studied chronons with a regularized form of Bose–Einstein statistics due to Tchavdar D. Palev.