Iterating reflection over intuitionistic arithmetic

Abstract: In this expository note, we study iterations of consistency, local and uniform reflection over $\mathbf{HA}$ (Heyting Arithmetic). In the case of uniform reflection, we give a new proof of Dragalin's extension of Feferman's completeness theorem to $\mathbf{HA}$. The treatment of uniform reflection is inspired by a proof of Feferman's completeness theorem due to Rathjen.