On the Orbits of Computable Enumerable Sets

On the Orbits of Computable Enumerable Sets

Cached

Download Links

by Peter A. Cholak , Rodney Downey , Leo , A. Harrington

Venue:	Submitted
Citations:	2 - 2 self

BibTeX

@ARTICLE{Cholak_onthe,
    author = {Peter A. Cholak and Rodney Downey and Leo and A. Harrington},
    title = {On the Orbits of Computable Enumerable Sets},
    journal = {Submitted},
    year = {},
    volume = {607264}
}

Bookmark

OpenURL

Abstract

Abstract. 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 1-complete. 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). 1.

Citations

714	Theory of recursive functions and effective computability, McGraw-Hill - Rogers - 1967
411	Recursively Enumerable Sets and Degrees - Soare - 1987
86	Higher recursion theory - Sacks - 1990
38	Computable structures and the hyperarithmetical hierarchy - Ash, Knight
30	Automorphisms of the lattice of recursively enumerable sets: Orbits - Downey, Stob - 1992
21	On the lattice of recursively enumerable sets - Lachlan - 1968
20	Post’s program and incomplete recursively enumerable sets - Harrington, Soare - 1991
19	Automorphisms of the lattice of recursively enumerable sets - Soare - 1974
12	The ∆ 0 3 -automorphism method and noninvariant classes of degrees - Harrington, Soare - 1996
11	Codable sets and orbits of computably enumerable sets - Harrington, Soare - 1998
11	On the orbit of hyperhypersimple sets - Maass - 1984
8	On the definability of the double jump in the computably enumerable sets - Cholak, Harrington
7	There is no fat orbit - Downey, Harrington - 1996
6	Some orbits for - Cholak, Downey, et al. - 2001
4	Isomorphisms of splits of computably enumerable sets - Cholak, Harrington
4	Extension theorems, orbits, and automorphisms of the computably enumerable sets - Cholak, Harrington
4	Jumps of hemimaximal sets - Downey, Stob - 1991
4	Characterizations for Computable Structures - White - 2000
4	Π1 1 relations and paths through O - Goncharov, Harizanov, et al.
3	Realizing levels of the hyperarithmetic hierarchy as degree spectra of relations on computable structures - Hirschfeldt, White - 2003
2	The Computably Enumerable Sets: the Past, the Present and the Future. Theory and Applications of Models of Computation, 2006, Beijing China, Slides can be found at http://www.nd.edu/ ∼cholak - Cholak - 2006
2	relations and paths through O - Goncharov, Harizanov, et al.
1	Slaman-Woodin conjecture - Slaman, Woodin - 1989