Proceedings of the National Academy of Sciencesâ€¦

1991

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 underâ€¦ (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 wayâ€¦ (More)

For T any completion of Peano Arithmetic and for n any positive integer, there is a model of T of size 2, with no (n + 1)-length sequence of indiscernibles. Hence the Hanf number for omitting typesâ€¦ (More)

We indicate how to fix an error in the proof of the main theorem of our original paper, pointed out to us by Yong Liu and Keng Meng Ng. The main result of our paper [1] read as follows: Main Theorem.â€¦ (More)

We prove an algebraic extension theorem for the computably enumerable sets, E . Using this extension theorem and other work we then show ifA and Ã‚ are automorphic via9 then they are automorphic via3â€¦ (More)