## 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 ℵ_{6}-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 |
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Journal | Forum of Mathematics, Sigma |

Volume | 5 |

DOIs | |

State | Published - 2017 |

### Bibliographical note

Publisher Copyright:© 2017 The Author(s).