Non-Uniformizable Sets of Second Projective Level With Countable Cross-Sections in the Form of Vitali Classes Sample Contracts

DOI: 10.1070/IM8521

Non-Uniformizable Sets of Second Projective Level With Countable Cross-Sections in the Form of Vitali Classes • March 17th, 2024

• Contract Type
  Non-Uniformizable Sets of Second Projective Level With Countable Cross-Sections in the Form of Vitali Classes
• Filed
  March 17th, 2024

Abstract. We use a countable-support product of invariant Jensen’s forc- ing notions to define a model of ZFC set theory in which the uniformization principle fails for some planar Π1 set all of whose vertical cross-sections are countable sets and, more specifically, Vitali classes. We also define a sub- model of that model, in which there exists a countable Π1 sequence of Vitali classes Pn whose union n Pn is not a countable set. Of course, the axiom of choice fails in this submodel.