More notions of forcing add a Souslin tree

Preprint, Other literature type English OPEN
Brodsky, Ari Meir; Rinot, Assaf;
  • Publisher: Duke University Press
  • Journal: issn: 0029-4527
  • Publisher copyright policies & self-archiving
  • Related identifiers: doi: 10.1215/00294527-2019-0011
  • Subject: Mathematics - Logic | microscopic approach | Radin forcing | outside guessing of clubs | Magidor forcing | Cohen forcing | Prikry forcing | Souslin-tree construction | parameterized proxy principle | Hechler forcing | 03E35 | 03E05 | square principle | 03E65 | Primary 03E05, Secondary 03E35, 05C05 | 05C05

An $\aleph _{1}$ -Souslin tree is a complicated combinatorial object whose existence cannot be decided on the grounds of ZFC alone. But fifteen years after Tennenbaum and Jech independently devised notions of forcing for introducing such a tree, Shelah proved that alrea... View more
  • References (22)
    22 references, page 1 of 3

    [AS83] Uri Abraham and Saharon Shelah. Forcing closed unbounded sets. J. Symbolic Logic, 48(3):643-657, 1983.

    [AAK16] Domink Adolf, Arthur W. Apter, and Peter Koepke. Singularizing Successor Cardinals by Forcing. Submitted, 2016.

    [BR15a] Ari Meir Brodsky and Assaf Rinot. A microscopic approach to Souslin-tree constructions. Part I. arXiv preprint arXiv:1601.01821, 2015.

    [BR15b] Ari Meir Brodsky and Assaf Rinot. Reduced powers of Souslin trees. arXiv preprint arXiv:1507.05651, 2015.

    [BR16] Ari Meir Brodsky and Assaf Rinot. A microscopic approach to Souslin-tree constructions. Part II. in preparation, 2016.

    [CFM01] James Cummings, Matthew Foreman, and Menachem Magidor. Squares, scales and stationary reflection. J. Math. Log., 1(1):35-98, 2001.

    [CS02] James Cummings and Ernest Schimmerling. Indexed squares. Israel J. Math., 131:61-99, 2002.

    [DJ74] Keith J. Devlin and Ha˙ vard Johnsbra˙ ten. The Souslin problem. Lecture Notes in Mathematics, Vol. 405. Springer-Verlag, Berlin, 1974.

    [DS95] Mirna D˘zamonja and Saharon Shelah. On squares, outside guessing of clubs and I<f [λ]. Fund. Math., 148(2):165-198, 1995.

    [FH16] Laura Fontanella and Yair Hayut. Square and Delta reflection. Ann. Pure Appl. Logic, 167(8):663-683, 2016.

  • Similar Research Results (4)
  • Metrics
Share - Bookmark