Dynamic Set Theory: Adding Natural Time to Sets and Specifying Space-Time Overlap

How to utilize the notion of time in the scientific modeling of reality has emerged as an open problem for decades. Set theory is commonly employed as a foundational system for mathematics. This paper develops dynamic set theory, which adds natural time to sets from the perspective of human perception. In general, given a universal set, the state of a dynamic set at a particular time is a subset of the universal set. Relations between two dynamic sets (e.g. subset) are defined for their comparison. Operations on dynamic sets (e.g. intersection and union) are constructed to allow various manipulations of dynamic sets, used to obtain new dynamic sets. We prove the algebraic properties of the operations and use them to establish equality and the subset relation between dynamic sets. In addition, an application of dynamic sets on space-time overlap for fighting epidemics is presented to demonstrate the possible use of dynamic sets in the real world.