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Free limits of forcing and more on Aronszajn trees

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Abstract

We prove that the Souslin Hypothesis does not imply “every Aron. (=Aronszajn) tree is special”. For this end we introduce variants of the notion “special Aron. tree”. We also introduce a limit of forcings bigger than the inverse limit, and prove it preserves properness and related notions not less than inverse limit, and the proof is easier in some respects.

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

    S. Shelah

Authors
  1. S. Shelah
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Additional information

The result was announced in [9].

The author thanks Uri Avraham for detecting many errors.

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Shelah, S. Free limits of forcing and more on Aronszajn trees. Israel J. Math. 38, 315–334 (1981). https://doi.org/10.1007/BF02762777

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  • DOI: https://doi.org/10.1007/BF02762777

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