Generalized R-Cohesiveness and the Arithmetical Hierarchy: A Correction to "Generalized Cohesiveness"
Journal of Symbolic Logic 67 (3):1078 - 1082 (2002)
| Abstract | For $X \subseteq \omega$ , let $\lbrack X \rbrack^n$ denote the class of all n-element subsets of X. An infinite set $A \subseteq \omega$ is called n-r-cohesive if for each computable function $f: \lbrack \omega \rbrack^n \rightarrow \lbrace 0, 1 \rbrace$ there is a finite set F such that f is constant on $\lbrack A - F \rbrack^n$ . We show that for each n ≥ 2 there is no $\prod_n^0$ set $A \subseteq \omega$ which is n-r-cohesive. For n = 2 this refutes a result previously claimed by the authors, and for n ≥ 3 it answers a question raised by the authors | |||||||||
| 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: 5,705 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesPhilip Welch (1986). The Natural Hierarchy and Quasi-Hierarchy of Constructibility Degrees. Journal of Symbolic Logic 51 (1):130-134.
James C. Owings Jr (1989). A Cardinality Version of Biegel's Nonspeedup Theorem. Journal of Symbolic Logic 54 (3):761-767.
Peter Nyikos & Leszek Piątkiewicz (1995). On the Equivalence of Certain Consequences of the Proper Forcing Axiom. Journal of Symbolic Logic 60 (2):431-443.
Tamara J. Hummel & Carl G. Jockusch Jr (2001). Ramsey's Theorem for Computably Enumerable Colorings. Journal of Symbolic Logic 66 (2):873-880.
Andrzej Nowik & Tomasz Weiss (2002). On the Ramseyan Properties of Some Special Subsets of 2ω and Their Algebraic Sums. Journal of Symbolic Logic 67 (2):547-556.
Tom Linton (1991). Countable Structures, Ehrenfeucht Strategies, and Wadge Reductions. Journal of Symbolic Logic 56 (4):1325-1348.
P. Komjáth (1991). A Set Mapping with No Infinite Free Subsets. Journal of Symbolic Logic 56 (4):1400-1402.
Tamara Hummel & Carl G. Jockusch Jr (1999). Generalized Cohesiveness. Journal of Symbolic Logic 64 (2):489-516.
Carl G. Jockusch & Tamara J. Lakins (2002). Generalized R-Cohesiveness and the Arithmetical Hierarchy: A Correction to "Generalized Cohesiveness". Journal of Symbolic Logic 67 (3):1078 - 1082.
Carl G. Jockusch Jr & Tamara J. Lakins (2002). Generalized R-Cohesiveness and the Arithmetical Hierarchy: A Correction to "Generalized Cohesiveness". Journal of Symbolic Logic 67 (3):1078 - 1082.
Analytics
Monthly downloads
Sorry, there are not enough data points to plot this chart.
|
Added to index2009-01-28Total downloads0Recent downloads (6 months)0How can I increase my downloads? |
My notes
Discussion
