Aronszajn trees, square principles, and stationary reflection

Mathematical Logic Quarterly 63 (3-4):265-281 (2017)

Abstract

We investigate questions involving Aronszajn trees, square principles, and stationary reflection. We first consider two strengthenings of math formula introduced by Brodsky and Rinot for the purpose of constructing κ-Souslin trees. Answering a question of Rinot, we prove that the weaker of these strengthenings is compatible with stationary reflection at κ but the stronger is not. We then prove that, if μ is a singular cardinal, math formula implies the existence of a special math formula-tree with a cf-ascent path, thus answering a question of Lücke.

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References found in this work

Set Theory.Keith J. Devlin - 1981 - Journal of Symbolic Logic 46 (4):876-877.
Squares, Scales and Stationary Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
Scales, Squares and Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (1):35-98.
Combinatorial Principles in the Core Model for One Woodin Cardinal.Ernest Schimmerling - 1995 - Annals of Pure and Applied Logic 74 (2):153-201.
Reflecting Stationary Sets.Menachem Magidor - 1982 - Journal of Symbolic Logic 47 (4):755-771.

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Citations of this work

A Microscopic Approach to Souslin-Tree Constructions, Part I.Ari Meir Brodsky & Assaf Rinot - 2017 - Annals of Pure and Applied Logic 168 (11):1949-2007.
Squares, Ascent Paths, and Chain Conditions.Chris Lambie-Hanson & Philipp Lücke - 2018 - Journal of Symbolic Logic 83 (4):1512-1538.
More Notions of Forcing Add a Souslin Tree.Ari Meir Brodsky & Assaf Rinot - 2019 - Notre Dame Journal of Formal Logic 60 (3):437-455.
A Microscopic Approach to Souslin-Tree Construction, Part II.Ari Meir Brodsky & Assaf Rinot - 2021 - Annals of Pure and Applied Logic 172 (5):102904.
Local Saturation and Square Everywhere.Monroe Eskew - 2020 - Journal of Mathematical Logic 20 (3):2050019.

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