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Infima in the recursively enumerable weak truth table degrees. (English) Zbl 0909.03038
The following interesting results are given:
1. For any nonrecursive, $$W$$-incomplete r.e. $$W$$-degree $${\mathbf c}$$, there is an r.e. $$W$$-degree $${\mathbf a} |_W {\mathbf c}$$ such that the infimum $${\mathbf a} \cap {\mathbf c}$$ exists. This shows that there are no strongly noncappable r.e. $$W$$-degrees, in contrast to the situation in the r.e. $$T$$-degrees.
2. For any nonrecursive, $$W$$-incomplete r.e. $$W$$-degree $${\mathbf c}$$, there is an r.e. $$W$$-degree $${\mathbf a}$$ such that the infimum $${\mathbf a} \cap {\mathbf c}$$ fails to exist.
##### MSC:
 03D25 Recursively (computably) enumerable sets and degrees
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##### References:
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