## Specializing Aronszajn trees with strong axiom A and Halving.(English)Zbl 1472.03060

Summary: 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 $\aleph_1=\mathfrak{d}< \operatorname{unif}({\mathcal{M}})=\aleph_2=2^{\omega}.$

### MSC:

 03E35 Consistency and independence results 03E15 Descriptive set theory 03E17 Cardinal characteristics of the continuum 03D65 Higher-type and set recursion theory

### Keywords:

proper forcing; bounding forcing; Aronszajn tree
Full Text:

### References:

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