  We discuss the building blocks for a consistent inclusion of chiral
three-nucleon (3N) interactions into ab initio nuclear structure calculations
beyond the lower p-shell. We highlight important technical developments, such
as the similarity renormalization group (SRG) evolution in the 3N sector, a
JT-coupled storage scheme for 3N matrix elements with efficient on-the-fly
decoupling, and the importance truncated no-core shell model with 3N
interactions. Together, these developments make converged ab initio
calculations with explicit 3N interactions possible also beyond the lower
p-shell. We analyze in detail the impact of various truncations of the
SRG-evolved Hamiltonian, in particular the truncation of the
harmonic-oscillator model space used for solving the SRG flow equations and the
omission of the induced beyond-3N contributions of the evolved Hamiltonian.
Both truncations lead to sizable effects in the upper p-shell and beyond and we
present options to remedy these truncation effects. The analysis of the
different truncations is a first step towards a systematic uncertainty
quantification of all stages of the calculation.
