: Many of the Internet's problems are related to names. There are many empirical ideas of the further development of naming on the Internet. However, there are no theoretical foundations for efficient development of such systems. In this paper, we take a unique approach to the naming problem in distributed environments. We place the naming problem in a mathematical context of named set theory and show a correlation between naming strategies for the Internet and named sets in mathematics. To achieve this goal, we give (in Section 2) a brief background in named set theory and then develop (in Section 3) an operation algebra on named sets related to problems of naming on the Internet and other distributed systems.