Infima in the recursively enumerable weak truth table degrees (Q1130238)

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.