Combinatorial operations on sets are almost never well defined on Turing degrees, a fact so obvious that counterexamples are worth exhibiting. The case we focus on is the symmetric-difference operator; there are pairs of (nonzero) degrees for which the symmetric-difference operation is well defined. Some examples can be extracted from the literature, e.g. from the existence of nonzero degrees with strong minimal covers. We focus on the case of incomparable r.e. degrees for which the symmetric-difference operation is well defined.

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可计算性和对称差分算子

集合上的组合运算几乎从来没有在图灵度上得到很好的定义，这一事实如此明显以至于值得展示反例。我们关注的案例是对称差分算子；有成对的（非零）度数，其对称差分运算是明确定义的。可以从文献中提取一些示例，例如从具有强最小覆盖的非零度的存在中提取。我们专注于对称差分运算定义良好的不可比较的 re 度的情况。