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 square(lambda)* + GCH entails the existence of a lambda(+)-Souslin tree, for a singular cardinal lambda. We provide an affirmative answer under the additional assumption that there exists a non-reflecting stationary subset of E-not equal cf(lambda)(lambda+). As a bonus, the outcome lambda(+)-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

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

Access to Document

10.1007/s11083-019-09482-7

Cite this

@article{ac7280f5941e43499f75c6731533f5ca,

title = "A Remark on Schimmerling's Question",

abstract = "Schimmerling asked whether square(lambda)* + GCH entails the existence of a lambda(+)-Souslin tree, for a singular cardinal lambda. We provide an affirmative answer under the additional assumption that there exists a non-reflecting stationary subset of E-not equal cf(lambda)(lambda+). As a bonus, the outcome lambda(+)-Souslin tree is moreover free.",

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

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

note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature B.V.",

year = "2019",

month = nov,

day = "1",

doi = "10.1007/s11083-019-09482-7",

language = "אנגלית",

volume = "36",

pages = "525--561",

journal = "Order",

issn = "0167-8094",

publisher = "Springer Netherlands",

number = "3",

}

TY - JOUR

T1 - A Remark on Schimmerling's Question

AU - Brodsky, Ari Meir

AU - Rinot, Assaf

PY - 2019/11/1

Y1 - 2019/11/1

N2 - Schimmerling asked whether square(lambda)* + GCH entails the existence of a lambda(+)-Souslin tree, for a singular cardinal lambda. We provide an affirmative answer under the additional assumption that there exists a non-reflecting stationary subset of E-not equal cf(lambda)(lambda+). As a bonus, the outcome lambda(+)-Souslin tree is moreover free.

AB - Schimmerling asked whether square(lambda)* + GCH entails the existence of a lambda(+)-Souslin tree, for a singular cardinal lambda. We provide an affirmative answer under the additional assumption that there exists a non-reflecting stationary subset of E-not equal cf(lambda)(lambda+). As a bonus, the outcome lambda(+)-Souslin tree is moreover free.

KW - Microscopic approach

KW - Parameterized proxy principle

KW - Weak square

KW - Postprocessing function

KW - Non-reflecting stationary set

KW - Free Souslin tree

KW - Specializable Souslin tree

KW - Complete tree

KW - Ascending path

UR - http://www.scopus.com/inward/record.url?scp=85076400718&partnerID=8YFLogxK

U2 - 10.1007/s11083-019-09482-7

DO - 10.1007/s11083-019-09482-7

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

SN - 0167-8094

VL - 36

SP - 525

EP - 561

JO - Order

JF - Order

IS - 3

ER -

A Remark on Schimmerling's Question

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this