We characterize the function of MHC molecules by the sets of pathogens that they recognize, which we call their "recognition sets." Two features of the MHC–pathogen interaction may be important to the theory of polymorphism construction at MHC loci: First, there may be a large degree of overlap, or degeneracy, among the recognition sets of MHC molecules. Second, when infected with a pathogen, an MHC genotype may have a higher fitness if that pathogen belongs to the overlapping portion, or intersection, of the two recognition sets of the host, when compared with a genotype that contains that pathogen in only one of its recognition sets. We call this benefit "intersection advantage," , and incorporate it, as well as the degree of recognition degeneracy, m, into a model of heterozygote advantage that utilizes a set-theoretic definition of fitness. Counterintuitively, we show that levels of polymorphism are positively related to m and that a high level of recognition degeneracy is necessary for polymorphism at MHC loci under heterozygote advantage. Increasing reduces levels of polymorphism considerably. Hence, if intersection advantage is significant for MHC genotypes, then heterozygote advantage may not explain the very high levels of polymorphism observed at MHC genes.