Aronszajn trees on א2 and א3

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Assuming the existence of a supercompact cardinal and a weakly compact cardinal above it, we provide a generic extension where there are no Aronszajn trees of height ω2 or ω3. On the other hand we show that some large cardinal assumptions are necessary for such a consistency result.

Original languageEnglish
Pages (from-to)213-230
Number of pages18
JournalAnnals of Pure and Applied Logic
Issue number3
StatePublished - 1 Jan 1983
Externally publishedYes


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