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Isomorphisms Of Splits Of Computably Enumerable Sets
 J. OF SYMBOLIC LOGIC
, 2002
"... We show that if A and A are automorphic via # then the structures SR (A) and SR ( 3 isomorphic via an isomorphism # induced by #. Then we use this result to classify completely the orbits of hhsimple sets. ..."
Abstract

Cited by 4 (4 self)
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We show that if A and A are automorphic via # then the structures SR (A) and SR ( 3 isomorphic via an isomorphism # induced by #. Then we use this result to classify completely the orbits of hhsimple sets.
On the Orbits of Computable Enumerable Sets
, 2007
"... The goal of this paper is to show there is a single orbit of the c.e. sets with inclusion, E, such that the question of membership in this orbit is Σ1 1complete. This result and proof have a number of nice corollaries: the Scott rank of E is ωCK 1 + 1; not all orbits are elementarily definable; th ..."
Abstract

Cited by 3 (3 self)
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The goal of this paper is to show there is a single orbit of the c.e. sets with inclusion, E, such that the question of membership in this orbit is Σ1 1complete. This result and proof have a number of nice corollaries: the Scott rank of E is ωCK 1 + 1; not all orbits are elementarily definable; there is no arithmetic description of all orbits of E; for all finite α ≥ 9, there is a properly ∆0 α orbit (from the proof).
The complexity of orbits of computably enumerable sets
 BULLETIN OF SYMBOLIC LOGIC
, 2008
"... The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, E, such that the question of membership in this orbit is Σ1 1complete. This result and proof have a number of nice corollaries: the Scott rank of E is ωCK 1 + 1; not all orbits are elementarily definable; ..."
Abstract

Cited by 2 (0 self)
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The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, E, such that the question of membership in this orbit is Σ1 1complete. This result and proof have a number of nice corollaries: the Scott rank of E is ωCK 1 + 1; not all orbits are elementarily definable; there is no arithmetic description of all orbits of E; for all finite α ≥ 9, there is a properly ∆0 α orbit (from the proof).