We study the relation of continuous reducibility, or Wadge reducibility, between subsets of an affine variety. We show that on any curve the relation of continuous reducibility is a bqo, though it may have large finite antichains. We determine the Wadge hierarchy on irreducible curves and on countable irreducible affine varieties of any dimension. Under a technical assumption of adequateness, we prove that on the class of finite differences of closed subsets of an irreducible affine variety the structure of the Wadge hierarchy depends only on the dimension of the affine variety and coincides with the difference hierarchy; we also show that this assumption of adequateness is satisfied by a large class of affine varieties. In contrast, we show that for large cardinalities the behaviour of the Wadge hierarchy outside the class of finite differences of closed sets can be much wilder, for example there may exist antichains of size the continuum.

我们研究仿射变种的子集之间的连续可还原性或Wadge可还原性的关系。我们表明，在任何曲线上，连续可还原性的关系都是bqo，尽管它可能具有较大的有限反链。我们在不可约曲线和任意维数不可约仿射变种上确定Wadge层次结构。在适当性的技术假设下，我们证明在不可约仿射变种的闭合子集的有限差分类上，Wadge层次结构仅取决于仿射变体的维数，并且与差异层次一致。我们还表明，足够的这种假设已被一大类仿射品种所满足。相比之下，