On the Orbits of Computably Enumerable Sets
| dc.creator | Cholak, Peter | |
| dc.creator | Downey, Rod | |
| dc.creator | Harrington, Leo | |
| dc.date | 2006-07-11 | |
| dc.date | 2007-11-21 | |
| dc.date.accessioned | 2026-07-07T08:44:05Z | |
| dc.date.available | 2026-07-07T08:44:05Z | |
| dc.description | The goal of this paper is to show there is a single orbit of the c.e. sets with inclusion, $\mathcal{E}$, such that the question of membership in this orbit is $Σ^1_1$-complete. This result and proof have a number of nice corollaries: The Scott rank of $\mathcal{E}$ is $ω^{CK}_1+1; Not all orbits are elementarily definable; There is no arithmetic description of all orbits of $\mathcal{E}$; For all finite $α\geq 9$, there is a properly $Δ^0_α$ orbit (from the proof). April 6, 2007, minor changes Nov 20, 2007, minor changes | |
| dc.identifier | https://arxiv.org/abs/math/0607264 | |
| dc.identifier | http://arxiv.org/abs/math/0607264 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142538 | |
| dc.subject | Logic | |
| dc.subject | 03D25 | |
| dc.title | On the Orbits of Computably Enumerable Sets | |
| dc.type | text |