Cichoń’s maximum without large cardinals

  • Martin Goldstern

    TU Wien, Austria
  • Jakob Kellner

    TU Wien, Austria
  • Diego A. Mejía

    Shizuoka University, Japan
  • Saharon Shelah

    Hebrew University of Jerusalem, Israel; Rutgers University, New Brunswick, USA
Cichoń’s maximum without large cardinals cover
Download PDF

This article is published open access under our Subscribe to Open model.


Cichoń’s diagram lists twelve cardinal characteristics (and the provable inequalities between them) associated with the ideals of null sets, meager sets, countable sets, and -compact subsets of the irrationals.

It is consistent that all entries of Cichoń’s diagram are pairwise different (apart from and , which are provably equal to other entries). However, the consistency proofs so far required large cardinal assumptions.

In this work, we show the consistency without such assumptions.

Cite this article

Martin Goldstern, Jakob Kellner, Diego A. Mejía, Saharon Shelah, Cichoń’s maximum without large cardinals. J. Eur. Math. Soc. 24 (2022), no. 11, pp. 3951–3967

DOI 10.4171/JEMS/1178