We first prove two theorems on the low(2) degrees and the join property in the local structure D(<= 0'): An r.e. degree is low(2) if and only if it is bounded by an r.e. degree without the join property (in D(<= 0')), and an FPF Delta(0)(2) degree is low(2) if and only if it fails to have the join property. We also study the join property in the global structure and show that for every array recursive degree, there is a degree above it which fails to satisfy the join property.
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