REDUCED POWERS of SOUSLIN TREES

Ari Meir Brodsky; Assaf Rinot

doi:10.1017/fms.2016.34

REDUCED POWERS of SOUSLIN TREES

Ari Meir Brodsky, Assaf Rinot

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

We study the relationship between κ-Souslin tree T and its reduced powers T^θ/u. Previous works addressed this problem from the viewpoint of a single power , whereas here, tools are developed for controlling different powers simultaneously. As a sample corollary, we obtain the consistency of an -Souslin tree and a sequence of uniform ultrafilters (μ_n | n < 6) such that T^ℵn 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.

Original language	English
Journal	Forum of Mathematics, Sigma
Volume	5
DOIs	https://doi.org/10.1017/fms.2016.34
State	Published - 1 Jan 2017

All Science Journal Classification (ASJC) codes

Analysis
Theoretical Computer Science
Algebra and Number Theory
Statistics and Probability
Mathematical Physics
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Mathematics

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title = "REDUCED POWERS of SOUSLIN TREES",

abstract = "We study the relationship between κ-Souslin tree T and its reduced powers Tθ/u. Previous works addressed this problem from the viewpoint of a single power , whereas here, tools are developed for controlling different powers simultaneously. As a sample corollary, we obtain the consistency of an -Souslin tree and a sequence of uniform ultrafilters (μn | n < 6) such that Tℵn 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.",

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N2 - We study the relationship between κ-Souslin tree T and its reduced powers Tθ/u. Previous works addressed this problem from the viewpoint of a single power , whereas here, tools are developed for controlling different powers simultaneously. As a sample corollary, we obtain the consistency of an -Souslin tree and a sequence of uniform ultrafilters (μn | n < 6) such that Tℵn 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.

AB - We study the relationship between κ-Souslin tree T and its reduced powers Tθ/u. Previous works addressed this problem from the viewpoint of a single power , whereas here, tools are developed for controlling different powers simultaneously. As a sample corollary, we obtain the consistency of an -Souslin tree and a sequence of uniform ultrafilters (μn | n < 6) such that Tℵn 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.

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DO - 10.1017/fms.2016.34

M3 - مقالة

SN - 2050-5094

VL - 5

JO - Forum of Mathematics, Sigma

JF - Forum of Mathematics, Sigma

ER -

REDUCED POWERS of SOUSLIN TREES

Abstract

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