Archive for Mathematical Logic 46 (7-8):679-693 (2008)

In this paper we first give a variant of a theorem of Jockusch–Lewis– Remmel on existence of a computable, degree-preserving homeomorphism between a bounded strong ${\Pi^0_2}$ class and a bounded ${\Pi^0_1}$ class in 2 ω . Namely, we show that for mathematically common and interesting topological spaces, such as computably presented ${\mathbb{R}^n}$ , we can obtain a similar result where the homeomorphism is in fact the identity mapping. Second, we apply this finding to give a new, priority-free proof of existence of a tree of shadow points computable in 0′
Keywords Computability theory  Recursion theory  Topology  Recursive analysis  Computable analysis  Recursive topology  Computable topology  Avoidable points  Shadow points
Categories (categorize this paper)
DOI 10.1007/s00153-007-0056-0
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 58,425
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

Π01-Classes and Rado's Selection Principle.C. G. Jockusch, A. Lewis & J. B. Remmel - 1991 - Journal of Symbolic Logic 56 (2):684 - 693.
A Blend of Methods of Recursion Theory and Topology.Iraj Kalantari & Larry Welch - 2003 - Annals of Pure and Applied Logic 124 (1-3):141-178.
$\Pi^0_1$-Classes And Rado's Selection Principle.C. G. Jockusch, A. Lewis & J. B. Remmel - 1991 - Journal of Symbolic Logic 56 (2):684-693.

View all 6 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

On Turing Degrees of Points in Computable Topology.Iraj Kalantari & Larry Welch - 2008 - Mathematical Logic Quarterly 54 (5):470-482.
Computability and Recursion.Robert I. Soare - 1996 - Bulletin of Symbolic Logic 2 (3):284-321.
On the Formal Points of the Formal Topology of the Binary Tree.Silvio Valentini - 2002 - Archive for Mathematical Logic 41 (7):603-618.
Recursive Approximability of Real Numbers.Xizhong Zheng - 2002 - Mathematical Logic Quarterly 48 (S1):131-156.
Borel Complexity and Computability of the Hahn–Banach Theorem.Vasco Brattka - 2008 - Archive for Mathematical Logic 46 (7-8):547-564.
Degrees of Unsolvability of Continuous Functions.Joseph S. Miller - 2004 - Journal of Symbolic Logic 69 (2):555 - 584.
Computability & Unsolvability.Martin Davis - 1958 - Dover Publications.
Weak Presentations of Computable Fields.Carl G. Jockusch & Alexandra Shlapentokh - 1995 - Journal of Symbolic Logic 60 (1):199 - 208.


Added to PP index

Total views
14 ( #687,327 of 2,420,865 )

Recent downloads (6 months)
1 ( #543,702 of 2,420,865 )

How can I increase my downloads?


My notes