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3 results

  • SQUARE WITH BUILT-IN DIAMOND-PLUS

  • ASSAF RINOT, RALF SCHINDLER
  • Journal:
    The Journal of Symbolic Logic / Volume 82 / Issue 3 / September 2017
    Published online by Cambridge University Press:
    08 September 2017, pp. 809-833
    Print publication:
    September 2017

  • We formulate combinatorial principles that combine the square principle with various strong forms of the diamond principle, and prove that the strongest amongst them holds in L for every infinite cardinal.

    As an application, we prove that the following two hold in L:

    1. 1. For every infinite regular cardinal λ, there exists a special λ+-Aronszajn tree whose projection is almost Souslin;

    2. 2. For every infinite cardinal λ, there exists a respecting λ+-Kurepa tree; Roughly speaking, this means that this λ+-Kurepa tree looks very much like the λ+-Souslin trees that Jensen constructed in L.

  • Guessing with Mutually Stationary Sets

  • Pierre Matet
  • Journal:
    Canadian Mathematical Bulletin / Volume 51 / Issue 4 / 01 December 2008
    Published online by Cambridge University Press:
    20 November 2018, pp. 579-583
    Print publication:
    01 December 2008
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  • We use the mutually stationary sets of Foreman and Magidor as a tool to establish the validity of the two-cardinal version of the diamond principle in some special cases.