Free limits of forcing and more on Aronszajn trees

S. Shelah

doi:10.1007/BF02762777

Free limits of forcing and more on Aronszajn trees

S. Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English
Pages (from-to)	315-334
Number of pages	20
Journal	Israel Journal of Mathematics
Volume	38
Issue number	4
DOIs	https://doi.org/10.1007/BF02762777
State	Published - Dec 1981

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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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AB - 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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Free limits of forcing and more on Aronszajn trees

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