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P-ideal dichotomy and a strong form of the Suslin Hypothesis

Volume 251 / 2020

Borisa Kuzeljevic, Stevo Todorcevic Fundamenta Mathematicae 251 (2020), 17-33 MSC: Primary 03E35; Secondary 03E05. DOI: 10.4064/fm864-2-2020 Published online: 19 June 2020

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.

Authors

  • Borisa KuzeljevicDepartment of Mathematics and Informatics
    Faculty of Sciences
    University of Novi Sad
    Trg Dositeja Obradovica 4
    21000 Novi Sad, Serbia
    e-mail
  • Stevo TodorcevicDepartment of Mathematics
    University of Toronto
    Toronto, Canada, M5S 2E4
    and
    Institut de Mathématiques de Jussieu
    UMR 7586
    2 pl. Jussieu, Case 7012
    75251 Paris Cedex 05, France
    and
    Mathematical Institute SANU
    Kneza Mihaila 36
    11001 Belgrade, Serbia
    e-mail
    e-mail

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