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A set A of nonnegative integers is recursively enumerable (r.e.) if A can be computably listed. It is shown that there is a first-order property, Q(X), definable in E, the lattice of r.e. sets under inclusion, such that (i) if A is any r.e. set satisfying Q(A) then A is nonrecursive and Turing incomplete and (ii) there exists an r.e. set A satisfying Q(A).… (More)
In 1969 Rabin introduced tree automata and proved one of the deepest decidability results. If you worked on decision problems you did most probably use Rabin's result. But did you make your way through Rabin's cumbersome proof with its induction on countable ordinals? Building on ideas of our predecessors-&-mdash;and especially those of… (More)
We show that if A and A are automorphic via then the structures S R (A) and S R (A) are 0 3-isomorphic via an isomorphism induced by. Then we use this result to classify completely the orbits of hhsimple sets.