In this paper, the authors announce some recent results on the computably enumerable (c.e.) sets. One set of results involves invariant classes and another set involves automorphisms of the c.e. sets. The proof of these results uses a new form of definable coding for the c.e. sets. One very interesting theorem is that \(\text{high}_n\) \((\overline{\text{low}_n})\) c.e. degrees are invariant for all \(n\geq 2\). This theorem solves the long standing Martin Invariance Conjecture; the conjecture is not true. Another interesting result about automorphisms of the c.e. sets is that any two hhsimple sets \(H_1\) and \(H_2\) are automorphic iff they are \(\Delta_3^0\)-automorphic iff \({\mathcal L}^*(H_1) \simeq _{\Delta_3^0} {\mathcal L}^*(H_2)\). This result completely characterizes when two hhsimple sets are automorphic.