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A set A is symmetric enumeration (se-) reducible to a set B (A≤se B) if A is enumeration reducible to B and A is enumeration reducible to B. This reducibility gives rise to a degree structure (Dse) whose least element is the class of computable sets. We give a classification of ≤se in terms of other standard reducibilities and we show that the natural embedding of the Turing degrees (D T ) into the enumeration degrees (De) translates to an embedding ( ιse ) into Dse that preserves leastdoi:10.1305/ndjfl/1179323263 fatcat:w3ja3qqvq5g2ddijphyzsllhny