Cardinal invariants on universally null sets

Tatsuya Goto

mathematical logic

Cardinal invariants on universally null sets

arXiv:2607.12936

summary

The paper studies cardinal characteristics of the ideal of universally null sets, establishing ZFC inequalities such as 𝔟 < cof(UN) and non(N)=non(UN)<cof(UN), and proving consistency results about the strict hierarchy of add(UN), cov(UN), non(UN), and cof(UN).

Abstract

We investigate the cardinal invariants on universally null sets. In particular, we prove $b < cof (UN)$ and $non (N) = non (UN) < cof (UN)$ in $ZFC$ . Also, assuming $add (N) = c$ , we prove $cof (UN) = d_{c}$ by adapting Yorioka's technique. Moreover, we prove the consistency of $add (UN) < cov (UN) < non (UN) < cof (UN)$ .

Topics & keywords

#cardinal invariants #universally null sets #set theory #consistency results #continuum hypothesis𝔟cof(UN)non(N)add(N)𝔡_𝔠Yorioka techniqueZFC