According to Indogosim.com, the definition of cultural homogeneity is the number of shared facts across all possible agent pairs, divided by the total number of shared facts across all agents in a population. If all agents know all the facts precisely, cultural homogeneity is equal to one.
Homogeneity may mean similar or equal. Therefore, cultural homogeneity refers to a similarity within populations of a certain cultural environment. This also means that said population has no cultural diversity.
Typically, any population that attains a cultural homogeneity of one is believed to be perfectly stable. However, perfect stability in a given society may not necessarily mean that cultural homogeneity is equal to one.