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SQUARE WITH BUILT-IN DIAMOND-PLUS

  • ASSAF RINOT (a1) and RALF SCHINDLER (a2)
Abstract
Abstract

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.

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

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.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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