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- Title
THE WADGE ORDER ON THE SCOTT DOMAIN IS NOT A WELL-QUASI-ORDER.
- Authors
DUPARC, JACQUES; VUILLEUMIER, LOUIS
- Abstract
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}_{emb} $ equipped with the order induced by homomorphisms is embedded into the Wadge order on the $\Delta _2^0 $ -degrees of the Scott domain. We then show that $\mathbb{P}_{emb} $ admits both infinite strictly decreasing chains and infinite antichains with respect to this notion of comparison, which therefore transfers to the Wadge order on the $\Delta _2^0 $ -degrees of the Scott domain.
- Subjects
DELTA State (Nigeria); BOREL sets; BOREL subsets; HOMOMORPHISMS; SET theory
- Publication
Journal of Symbolic Logic, 2020, Vol 85, Issue 1, p300
- ISSN
0022-4812
- Publication type
Article
- DOI
10.1017/jsl.2019.51