A NOTE ON BOUNDED-TRUTH-TABLE REDUCIBILITY

Bounded-truth-table and truth-table reducibilities are shown by Post to be distinct relations over the recursively enumerable, nonrecursive sets. In [2] and in [6], respectively, Dekker shows that one-one and many-one reducibilities differ on these sets and that truth-table and Turing reducibilities are distinct. This note will show that many-one and bounded-truth-table reducibilities also differ on these sets. Since the five reducibilities given are linearly ordered under implication (if A < 1B, then A <mB, if A <mB, then A< bttB, etc.), the conclusion that all five reducibilities are distinct on the recursively enumerable, nonrecursive sets will follow. A second theorem will provide an example of a recursively enumerable bounded-truth-table degree of unsolvability which contains infinitely many distinct many-one degrees.