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Major subsets and automorphisms of recursively enumerable sets

In Anil Nerode & Richard A. Shore (eds.), Recursion Theory. American Mathematical Society. pp. 21 (1985)

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  1. Effectively Inseparable Boolean Algebras in Lattices of Sentences.V. Yu Shavrukov - 2010 - Archive for Mathematical Logic 49 (1):69-89.
    We show the non-arithmeticity of 1st order theories of lattices of Σ n sentences modulo provable equivalence in a formal theory, of diagonalizable algebras of a wider class of arithmetic theories than has been previously known, and of the lattice of degrees of interpretability over PA. The first two results are applications of Nies’ theorem on the non-arithmeticity of the 1st order theory of the lattice of r.e. ideals on any effectively dense r.e. Boolean algebra. The theorem on degrees of (...)
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  • Definable Structures in the Lattice of Recursively Enumerable Sets.E. Herrmann - 1984 - Journal of Symbolic Logic 49 (4):1190-1197.
    It will be shown that in the lattice of recursively enumerable sets one can define elementarily with parameters a structure isomorphic to (∑ 0 4 , ∑ 0 3 ), i.e. isomorphic to the lattice of ∑ 0 4 sets together with a unary predicate selecting out exactly the ∑ 0 3 sets.
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