  We show that $\beth_{(2^{\operatorname{LS}({\bf K})})^+}$ is the lower bound
to the Hanf numbers for the length of the order property and for stability in
stable abstract elementary classes (AECs). Our examples satisfy the joint
embedding property, no maximal model, $(<\aleph_0)$-tameness but not
necessarily the amalgamation property. We also define variations on the order
and syntactic order properties by allowing the index set to be linearly ordered
rather than well-ordered. Combining with Shelah's stability theorem, we deduce
that our examples can have the order property up to any
$\mu<\beth_{(2^{\operatorname{LS}({\bf K})})^+}$. Boney conjectured that the
need for joint embedding property for two type-counting lemmas is necessary. We
solved the conjecture by showing it is independent of ZFC. Using Galois
Morleyization, we give syntactic proofs to known stability results assuming a
monster model.
