Abstract
Motivated by showing that in ZFC we cannot construct a special Aronszajn tree on some cardinal greater than \({\aleph _1}\), we produce a model in which the approachability property fails (hence there are no special Aronszajn trees) at all regular cardinals in the interval \(\left[ {{\aleph _2},{\aleph _{{\omega ^2} + 3}}} \right]\) and \({{\aleph _{{\omega ^2}}}}\) is strong limit.
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