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We prove a version of uniqueness theorem for Cuntz-Pimsner algebras ofdiscrete product systems over semigroups of Ore type. To this end, we introduceDoplicher-Roberts picture of Cuntz-Pimsner algebras, and the semigroup dual toa product system of 'regular' C*-correspondences. Under a certain aperiodicitycondition on the latter, we obtain the uniqueness theorem and a simplicitycriterion for the algebras in question. These results generalize thecorresponding ones for crossed products by discrete groups, due to Archbold andSpielberg, and for Exel's crossed products, due to Exel and Vershik. They alsogive interesting conditions for topological higher rank graphs and $P$-graphs,and apply to the new Cuntz C*-algebra $\mathcal{Q}_\mathbb{N}$ arising from the"$ax+b$"-semigroup over $\mathbb{N}$.

Topological aperiodicity for product systems over semigroups of Ore type