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Fundamenta MathematicaeVolume 251, Issue 1, 2020, Pages 17-34

P-ideal dichotomy and a strong form of the suslin hypothesis(Article)

  • Kuzeljevic, B.,
  • Todorcevic, S.
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  • aDepartment of Mathematics and Informatics, Faculty of Sciences, University of Novi, Sad Trg Dositeja Obradovica 4, Novi Sad, 21000, Serbia
  • bDepartment of Mathematics, University of Toronto, Toronto, M5S 2E4, Canada
  • cInstitut de Mathématiques de Jussieu UMR 7586, 2 pl. Jussieu, Case 7012, Paris Cedex 05, 75251, France
  • dMathematical Institute SANU, Kneza Mihaila 36, Belgrade, 11001, Serbia

Abstract

We introduce a forcing notion which forces the P-ideal dichotomy, while every almost Suslin tree from the ground model remains non-special. Thus, while the P-ideal dichotomy implies the Suslin Hypothesis, or equivalently that every Aronszajn tree has an uncountable antichain, it does not imply that every Aronszajn tree has a stationary antichain. © Instytut Matematyczny PAN, 2020

Author keywords

Almost Suslin treeP-ideal dichotomySpecial Aronszajn tree

Funding details

Funding sponsor Funding number Acronym
Natural Sciences and Engineering Research Council of Canada
See opportunities by NSERC		455916NSERC
Centre National de la Recherche ScientifiqueUMR7585CNRS

  • 1

    The first author was partially supported by the MPNTR grant ON174006. The second author was partially supported by the NSERC grant 455916 and the CNRS grant UMR7585.

  • ISSN: 00162736
  • Source Type: Journal
  • Original language: English
  • DOI: 10.4064/fm864-2-2020
  • Document Type: Article
  • Publisher: Institute of Mathematics. Polish Academy of Sciences


© Copyright 2020 Elsevier B.V., All rights reserved.

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Full Souslin trees at small cardinals
(2024) Journal of the London Mathematical Society
Yorioka, T.
Two chain conditions and their Todorčević's fragments of Martin's Axiom
(2024) Annals of Pure and Applied Logic
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