Recursively enumerable generic sets
Journal of Symbolic Logic 47 (4):809-823 (1982)
| Abstract | We show that one can solve Post's Problem by constructing generic sets in the usual set theoretic framework applied to tiny universes. This method leads to a new class of recursively enumerable sets: r.e. generic sets. All r.e. generic sets are low and simple and therefore of Turing degree strictly between 0 and 0'. Further they supply the first example of a class of low recursively enumerable sets which are automorphic in the lattice E of recursively enumerable sets with inclusion. We introduce the notion of a promptly simple set. This describes the essential feature of r.e. generic sets with respect to automorphism constructions | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,672 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesNoam Greenberg (2005). The Role of True Finiteness in the Admissible Recursively Enumerable Degrees. Bulletin of Symbolic Logic 11 (3):398-410.
E. Herrmann (1983). Orbits of Hyperhypersimple Sets and the Lattice of ∑03 Sets. Journal of Symbolic Logic 48 (3):693 - 699.
Richard A. Shore (1978). Nowhere Simple Sets and the Lattice of Recursively Enumerable Sets. Journal of Symbolic Logic 43 (2):322-330.
Steffen Lempp & Theodore A. Slaman (1989). A Limit on Relative Genericity in the Recursively Enumerable Sets. Journal of Symbolic Logic 54 (2):376-395.
Peter Cholak (1995). Automorphisms of the Lattice of Recursively Enumerable Sets. American Mathematical Society.
Stephan Wehner (1999). On Recursive Enumerability with Finite Repetitions. Journal of Symbolic Logic 64 (3):927-945.
E. Herrmann (1984). Definable Structures in the Lattice of Recursively Enumerable Sets. Journal of Symbolic Logic 49 (4):1190-1197.
Iraj Kalantari & Allen Retzlaff (1979). Recursive Constructions in Topological Spaces. Journal of Symbolic Logic 44 (4):609-625.
A. M. Dawes (1982). Splitting Theorems for Speed-Up Related to Order of Enumeration. Journal of Symbolic Logic 47 (1):1-7.
Wolfgang Maass (1984). On the Orbits of Hyperhypersimple Sets. Journal of Symbolic Logic 49 (1):51-62.
Analytics
Monthly downloads
Sorry, there are not enough data points to plot this chart.
|
Added to index2009-01-28Total downloads2 ( #232,382 of 549,051 )Recent downloads (6 months)1 ( #63,185 of 549,051 )How can I increase my downloads? |
My notes
Discussion
