Scott域上的Wadge序不是良拟序
The Wadge order on the Scott domain is not a well-quasi-order
摘要：
我们证明了Scott域的Borel子集的Wadge序不是良拟序，并且这一特征甚至出现在Borel秩至多为2的集合中。为此，将一类特殊的可数2-色偏序集$\mathbb{P}_{lay}$嵌入到Scott整环的$\boldsymbolΔ^0_2$ -度上的Wadge序中.然后，我们表明，$\mathbb{P}_{lay}$都承认无限严格减少链和无限反链相对于这个概念的比较，因此转移到Wadge秩序上的$\boldsymbolΔ^0_2$ -度的斯科特域。
英文摘要：
We prove that the Wadge order on the Borel subsets of the Scott domain is not a well-quasi-order, and that this feature even occurs among the sets of Borel rank at most 2. For this purpose, a specific class of countable 2-colored posets $\mathbb{P}_{lay}$ equipped with the order induced by homomorphisms is embedded into the Wadge order on the $\boldsymbolΔ^0_2$-degrees of the Scott domain. We then show that $\mathbb{P}_{lay}$ both admits infinite strictly decreasing chains and infinite antichains with respect to this notion of comparison, which therefore transfers to the Wadge order on the $\boldsymbolΔ^0_2$-degrees of the Scott domain.
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