The strong weak truth table (sw) reducibility was suggested by Downey, Hirschfeldt and LaForte as a measure of relative randomness. In this paper, in order to discuss the structure of sw-degrees further, we introduce the definition of sw-cuppable for c.e. reals. For c.e reals, it is natural to conclude that there exist sw-cuppable c.e. reals. The main result of this paper is that there exists an sw-cuppable strongly c.e. real.
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