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

Department of Mathematics

Ariel University

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

4 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

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature B.V.

Funding

Microscopic approach Parameterized proxy principle Weak square Postprocessing function Non-reflecting stationary set Free Souslin tree Specializable Souslin tree Complete tree Ascending path Israel Science Foundation https://doi.org/10.13039/501100003977 1630/14 Rinot Assaf Ministry of Aliyah and Immigrant Absorption https://doi.org/10.13039/501100003289 — Brodsky Ari Meir European Research Council https://doi.org/10.13039/501100000781 ERC-2018-StG 802756 Rinot Assaf Israel Science Foundation https://doi.org/10.13039/501100003977 2066/18 Rinot Assaf publisher-imprint-name Springer volume-issue-count 3 issue-article-count 15 issue-toc-levels 0 issue-pricelist-year 2019 issue-copyright-holder Springer Nature B.V. issue-copyright-year 2019 article-contains-esm No article-numbering-style ContentOnly article-registration-date-year 2019 article-registration-date-month 1 article-registration-date-day 25 article-toc-levels 0 toc-levels 0 volume-type Regular journal-product NonStandardArchiveJournal numbering-style ContentOnly article-grants-type Regular metadata-grant OpenAccess abstract-grant OpenAccess bodypdf-grant Restricted bodyhtml-grant Restricted bibliography-grant Restricted esm-grant OpenAccess online-first false pdf-file-reference BodyRef/PDF/11083_2019_Article_9482.pdf target-type OnlinePDF pdf-file-reference BodyRef/PDF/11083_2019_9482_TEX.zip target-type TEX issue-online-date-year 2019 issue-online-date-month 12 issue-online-date-day 3 issue-print-date-year 2019 issue-print-date-month 12 issue-print-date-day 3 issue-type Regular article-type OriginalPaper journal-subject-primary Mathematics journal-subject-secondary Order, Lattices, Ordered Algebraic Structures journal-subject-secondary Discrete Mathematics journal-subject-secondary Algebra journal-subject-collection Mathematics and Statistics open-access false The first author was supported by the Center for Absorption in Science, Ministry of Aliyah and Integration, State of Israel. The second author was partially supported by the European Research Council (grant agreement ERC-2018-StG 802756) and by the Israel Science Foundation (grant agreement 2066/18). We thank the anonymous referee for a careful reading of this paper and for providing valuable feedback. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. The first author was supported by the Center for Absorption in Science, Ministry of Aliyah and Integration, State of Israel. The second author was partially supported by the European Research Council (grant agreement ERC-2018-StG 802756) and by the Israel Science Foundation (grant agreement 2066/18). We thank the anonymous referee for a careful reading of this paper and for providing valuable feedback.

Funders	Funder number
Center for Absorption in Science
ERC-2018-StG	2019_9482_TEX.zip, BodyRef/PDF/11083_2019_Article_9482.pdf
Ministry of Aliyah and Integration, State of Israel
Parameterized
Horizon 2020 Framework Programme
European Commission	802756
Ministry of Aliyah and Immigrant Absorption
Israel Science Foundation	2066/18, https://doi.org/10.13039/501100003977
Ministry of Health, State of Israel
https://doi.org/10.13039/501100003977 1630/14

Keywords

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

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10.1007/s11083-019-09482-7

Cite this

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A Remark on Schimmerling’s Question

Abstract

Bibliographical note

Funding

Keywords

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