  Menger conjectured that subsets of R with the Menger property must be
${\sigma}$-compact. While this is false when there is no restriction on the
subsets of R, for projective subsets it is known to follow from the Axiom of
Projective Determinacy, which has considerable large cardinal consistency
strength. We note that in fact, Menger's conjecture for projective sets has
consistency strength of only an inaccessible cardinal.
