Notre Dame Journal of Formal Logic

Specializing Aronszajn Trees with Strong Axiom A and Halving

Heike Mildenberger and Saharon Shelah

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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 1=d<unif(M)=2=2ω.

Article information

Source
Notre Dame J. Formal Logic, Volume 60, Number 4 (2019), 587-616.

Dates
Received: 28 November 2016
Accepted: 22 June 2018
First available in Project Euclid: 25 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1569376826

Digital Object Identifier
doi:10.1215/00294527-2019-0021

Subjects
Primary: 03E15: Descriptive set theory [See also 28A05, 54H05] 03E17: Cardinal characteristics of the continuum
Secondary: 03E35: Consistency and independence results 03D65: Higher-type and set recursion theory

Keywords
proper forcing bounding forcing Aronszajn tree

Citation

Mildenberger, Heike; Shelah, Saharon. Specializing Aronszajn Trees with Strong Axiom A and Halving. Notre Dame J. Formal Logic 60 (2019), no. 4, 587--616. doi:10.1215/00294527-2019-0021. https://projecteuclid.org/euclid.ndjfl/1569376826


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