Specializing Aronszajn Trees with Strong Axiom A and Halving

Abstract

We construct creature forcings with strong Axiom A that specialize a given Aronszajn tree. We work with tree creature forcing. The creatures that live on the Aronszajn tree are normed and have the halving property. We show that our models fulfill $${\aleph }_1=\mathfrak{d}<unif(\mathcal{M})={\aleph }_2=2^{\omega }.$$