The quantum anomaly that breaks the U(1) axial symmetry of massless multi-flavored QCD leaves behind a discrete flavor-singlet chiral invariance. With massive quarks, this residual symmetry has a close connection with the strong CP-violating parameter theta. One result is that if the lightest quarks are degenerate, then a first order transition will occur when theta passes through pi. The resulting framework helps clarify when the rooting prescription for extrapolating in the number of flavors is valid.

12 pages, 7 figures. Contribution to the International Workshop on QCD Green's Functions, Confinement and Phenomenology September 7-11, 2009, ECT Trento, Italy. Revised version adds references