English

Of Mice and Machetes

Logic 2024-08-01 v1

Abstract

Let RR be the class of regular cardinals which are not hyperinaccessible. We show that L[R]L[R], and similar inner models in the α\alpha-inaccessible hierarchy, can be generated by iterating a small "machete" mouse up through all the ordinals, and then taking a generic extension by a hyperclass Magidor iteration of Prikry forcings. We then show that such simple mice are themselves elements of L[Reg]L[\mathsf{Reg}].

Cite

@article{arxiv.2407.21562,
  title  = {Of Mice and Machetes},
  author = {Christopher Henney-Turner and Philip Welch},
  journal= {arXiv preprint arXiv:2407.21562},
  year   = {2024}
}

Comments

21 pages

R2 v1 2026-06-28T17:59:16.786Z