There are no 𝑄-points in Laver’s model for the Borel conjecture

Abstract

It is shown that it is consistent with ZFC that no nonprincipal ultrafilter on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="omega"> <mml:semantics> <mml:mi>ω</mml:mi> <mml:annotation encoding="application/x-tex">\omega</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a <italic>Q</italic>-point (also called a rare ultrafilter).