English

On Petr Novikov's problem of ordered systems of uniform sets

Logic 2026-04-16 v3

Abstract

We prove that every ordinal α<ω2\alpha<\omega_2 is the order type of a certain system of uniform Borel sets in the sense of a well-ordering relation defined by Petr Novikov. This result gives a positive answer to a problem posed by Nicolas Luzin in 1935.

Keywords

Cite

@article{arxiv.2604.07594,
  title  = {On Petr Novikov's problem of ordered systems of uniform sets},
  author = {Vladimir Kanovei and Vassily Lyubetsky},
  journal= {arXiv preprint arXiv:2604.07594},
  year   = {2026}
}

Comments

13 pages