A generalization of the limit lemma and clopen games

Journal of Symbolic Logic 51 (2):273-291 (1986)
We give a new characterization of the hyperarithmetic sets: a set X of integers is recursive in e α if and only if there is a Turing machine which computes X and "halts" in less than or equal to the ordinal number ω α of steps. This result represents a generalization of the well-known "limit lemma" due to J. R. Shoenfield [Sho-1] and later independently by H. Putnam [Pu] and independently by E. M. Gold [Go]. As an application of this result, we give a recursion theoretic analysis of clopen determinacy: there is a correlation given between the height α of a well-founded tree corresponding to a clopen game $A \subseteq \omega^\omega$ and the Turing degree of a winning strategy f for one of the players--roughly, f can be chosen to be recursive in 0 α and this is the best possible (see § 4 for precise results)
Keywords Limit lemma   clopen games   hyperarithmetic winning strategy   trees
Categories (categorize this paper)
DOI 10.2307/2274051
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 24,463
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA
Keh-Hsun Chen (1978). Recursive Well-Founded Orderings. Annals of Mathematical Logic 13 (2):117-147.
D. -H. Chen (1978). Recursice Well-Founded Orderings. Annals of Pure and Applied Logic 13 (2):117.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

7 ( #500,352 of 1,925,541 )

Recent downloads (6 months)

1 ( #418,152 of 1,925,541 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.