In 1981, building on work by Ellentuck in 1974, Sageev showed ("A model of ZF + there exists an inaccessible, in which the Dedekind cardinals constitute a natural non-standard model of arithmetic," http://www.sciencedirect.com/science/article/pii/0003484381900176) that it is consistent relative to ZF + an inaccessible that the set of Dedekind finite cardinals is linearly ordered - and hence by Ellentuck forms an elementary extension of $\mathbb{N}$.

On page 223 of his paper, Sageev writes:

"In our construction it is necessary to assume that $\kappa$ is inaccessible. It is unknown to the author whether this result is actually bound up with a large cardinal assumption."

My question is:

- Is Sageev's result known to be equiconsistent with an inaccessible?