A Remark on Schimmerling’s Question

Ari Meir Brodsky; Assaf Rinot

doi:10.1007/s11083-019-09482-7

A Remark on Schimmerling’s Question

Ari Meir Brodsky, Assaf Rinot

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

3 Scopus citations

Abstract

Schimmerling asked whether □λ∗+GCH entails the existence of a λ⁺-Souslin tree, for a singular cardinal λ. We provide an affirmative answer under the additional assumption that there exists a non-reflecting stationary subset of E≠cf(λ)λ+. As a bonus, the outcome λ⁺-Souslin tree is moreover free.

Original language	English
Pages (from-to)	525-561
Number of pages	37
Journal	Order
Volume	36
Issue number	3
DOIs	https://doi.org/10.1007/s11083-019-09482-7
State	Published - 1 Nov 2019
Externally published	Yes

Keywords

Ascending path
Complete tree
Free Souslin tree
Microscopic approach
Non-reflecting stationary set
Parameterized proxy principle
Postprocessing function
Specializable Souslin tree
Weak square

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology
Computational Theory and Mathematics

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10.1007/s11083-019-09482-7

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title = "A Remark on Schimmerling{\textquoteright}s Question",

abstract = "Schimmerling asked whether □λ∗+GCH entails the existence of a λ+-Souslin tree, for a singular cardinal λ. We provide an affirmative answer under the additional assumption that there exists a non-reflecting stationary subset of E≠cf(λ)λ+. As a bonus, the outcome λ+-Souslin tree is moreover free.",

keywords = "Ascending path, Complete tree, Free Souslin tree, Microscopic approach, Non-reflecting stationary set, Parameterized proxy principle, Postprocessing function, Specializable Souslin tree, Weak square",

author = "Brodsky, {Ari Meir} and Assaf Rinot",

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AU - Rinot, Assaf

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AB - Schimmerling asked whether □λ∗+GCH entails the existence of a λ+-Souslin tree, for a singular cardinal λ. We provide an affirmative answer under the additional assumption that there exists a non-reflecting stationary subset of E≠cf(λ)λ+. As a bonus, the outcome λ+-Souslin tree is moreover free.

KW - Ascending path

KW - Complete tree

KW - Free Souslin tree

KW - Microscopic approach

KW - Non-reflecting stationary set

KW - Parameterized proxy principle

KW - Postprocessing function

KW - Specializable Souslin tree

KW - Weak square

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A Remark on Schimmerling’s Question

Abstract

Keywords

ASJC Scopus subject areas

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