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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
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References:

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