Let A⊕B =defn {2x | x ∈ A}∪{2x+1 | x ∈ B} be the computable join of A and B. Show that for all A,B ⊆ N i) A ≤m A ⊕ B and B ≤m A ⊕ B, and ii) If A ≤m C and B ≤m C then A ⊕ B ≤m C.


Let A⊕B =defn {2x | x ∈ A}∪{2x+1 | x ∈ B} be the computable join of A and B.


Show that for all A,B ⊆ N


i) A ≤m A ⊕ B and B ≤m A ⊕ B, and
ii) If A ≤m C and B ≤m C then A ⊕ B ≤m C.

Mar 12, 2021
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