  We exposit two previously unpublished theorems of Leo Harrington. The first
theorem says that there exist arithmetical singletons which are arithmetically
incomparable. The second theorem says that there exists a ranked point which is
not an arithmetical singleton. Unlike Harrington's proofs of these theorems,
our proofs do not use the finite- or infinite-injury priority method. Instead
they use an oracle construction adapted from the standard proof of the
Friedberg Jump Theorem.
