Lattice initial segments of the hyperdegrees
نویسندگان
چکیده
منابع مشابه
Lattice initial segments of the hyperdegrees
We a¢ rm a conjecture of Sacks [1972] by showing that every countable distributive lattice is isomorphic to an initial segment of the hyperdegrees, Dh. In fact, we prove that every sublattice of any hyperarithmetic lattice (and so, in particular, every countable locally nite lattice) is isomorphic to an initial segment of Dh. Corollaries include the decidability of the two quanti er theory of ...
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The study of the lattice E of computably enumerable sets under inclusion has been one of the central tasks of computability theory since the 1960's. We investigate initial segments of the lattice L of 0 1 classes (of sets) under inclusion and we compare this lattice with E. It was recently proved by Nies that the theory of each interval of the lattice E which is not a boolean algebra interprets...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2010
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1264433911