Complexity of hereditarily decomposable continua

The purpose of this short note is to show that the set of hereditarily decomposable subcontinua of In (2≤n≤ω) is a coanalytic and non-Borel subset of C(In), the space of all subcontinua of In endowed with the Hausdorff metric. As a simple corollary to this result, we obtain that there is no model for A, the set of arcwise connected continua in In.