  We introduce a family of Markov processes on set partitions with a bounded
number of blocks, called Lipschitz partition processes. We construct these
processes explicitly by a Poisson point process on the space of Lipschitz
continuous maps on partitions. By this construction, the Markovian consistency
property is readily satisfied; that is, the finite restrictions of any
Lipschitz partition process comprise a compatible collection of finite state
space Markov chains. We further characterize the class of exchangeable
Lipschitz partition processes by a novel set-valued matrix operation.
