Rathjen proved that Aczel's constructive set theory $\mathbf{CZF}$ extended with inaccessible sets of all transfinite orders can be interpreted in Martin-Löf type theory $\mathbf{MLTT}$ extended with Setzer's Mahlo universe and another universe above it. In this paper we show that this interpretation can be carried out bottom-up without the universe above the Mahlo universe, provided we add an accessibility predicate instead. If we work in Martin-Löf type theory with extensional identity types the accessibility predicate can be defined in terms of $\mathrm{W}$-types. The main part of our interpretation has been formalised in the proof assistant Agda.

@article{paperbot3355,
  title = {Interpretation of Inaccessible Sets in Martin-Löf Type Theory with One Mahlo Universe},
  author = {Yuta Takahashi},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 21, Issue 4},
  year = {2025},
  doi = {10.46298/lmcs-21(4:16)2025}
}