Electronic Resource
Springer
Archive for mathematical logic
26 (1987), S. 127-136
ISSN:
1432-0665
Keywords:
03 D 25
;
Weak truth table degrees
;
cap
;
cup
;
strong antisplitting property
;
contiguous degrees
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract LetA be an r.e. nonrecursive set. We sayA has thestrong antisplitting property if there exists an r.e. setB with 0〈 T B〈 T A such that ifA 1 ∪A 2=A andA 1∩A 2=0 thenA 1≦ T B impliesA 1≡ T 0 andB≦ T A 1 impliesA 1≡ T A. It is shown that below any high r.e. degree there exists an r.e. set with the strong antisplitting property. The main ingredient of the proof is a “localization” of Ambos-Spies' result that the “cup or cap” theorem fails forW-degrees.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02017497
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