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

Mildenberger, Heike; Shelah, Saharon

Notre Dame J. Formal Logic 60, No. 4, 587-616 (2019).

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

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