which is an ordinal between 1 and ω1, first defined by Pyatetskii-Shapiro. Nowadays the research of sets of uniqueness is just as much a branch of descriptive set theory as it is of harmonic analysis. See the Kechris-Louveau book referenced below. References Paul J. Cohen (1958), Topics in the theory of uniqueness of trigonometrical series , http://www.lix.polytechnique.fr/Labo/Ilan.Vardi/cohen.ps Alexander S. Kechris and Alain Louveau (1987), Descriptive set theory and the structure of sets of uniqueness (London Mathematical Society lecture series 128), Cambridge University Press. . Jean-Pierre Kahane and Raphaël Salem (1994), Ensembles parfaits et séries trigonométriques, Hermann, Paris. (in French). Harmonic analysis Fourier analysis