Erratum to "The primes contain arbitrarily long polynomial progressions" (Acta Math., (2008), 201, (213-305), 10.1007/s11511-008-0032-5)

In our previous paper "The primes contain arbitrarily long polynomial progressions" [Acta Math., 201 (2008), 213-305] there were some minor errors in our definition of the polynomial forms and polynomial correlation conditions, which is unreasonably strong as written due to the overly loose bound on the degree of the polynomials involved. In this erratum we repair this issue by capping the degree of the polynomials more strongly, and adjusting some other relevant components of the argument accordingly.