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- Title
REDUCED POWERS OF SOUSLIN TREES.
- Authors
BRODSKY, nARI MEIR; RINOT, ASSAF
- Abstract
We study the relationship between a κ-Souslin tree T and its reduced powers T θ /u. Previous works addressed this problem from the viewpoint of a single power θ, whereas here, tools are developed for controlling different powers simultaneously. As a sample corollary, we obtain the consistency of an ℵ6-Souslin tree T and a sequence of uniform ultrafilters <un∣ n < 6> such that T ℵn /un is ℵ6-Aronszajn if and only if n < 6 is not a prime number. This paper is the first application of the microscopic approach to Souslin-tree construction, recently introduced by the authors. A major component here is devising a method for constructing trees with a prescribed combination of freeness degree and ascent-path characteristics.
- Subjects
POWER law (Mathematics); PRIME numbers; ULTRAFILTERS (Mathematics); DEGREES of freedom; CARDINAL numbers
- Publication
Forum of Mathematics, Sigma, 2017, Vol 5, p1
- ISSN
2050-5094
- Publication type
Article
- DOI
10.1017/fms.2016.34