Borel ideals vs. Borel sets of countable relations and trees
For \(\mu\), a countable ordinal, let \(I_{\mu}\) be the ideal of subsets of \(\omega^{\mu}\) with order type less than \(\omega^{\mu}\). It is shown that, when appropriately coded, \(I_{\mu}\) is a \(\Sigma^ 0_{2\mu}\)-complete Borel set. This result is extended to partial orders representing small ordinals, trees with small ranks, etc. The proofs are based on Wadge games.
partial orders representing small ordinals
scientific article; zbMATH DE number 4101183
scientific article