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The two-cardinal problem for languages of arbitrary cardinality. (English) Zbl 1201.03018
Let \(\mathcal L\) be a first-order language of cardinality \(\kappa^{++}\) with a distinguished unary predicate \(U\). Under the assumption \(V=L\) (Gödel’s Axiom of Constructibility), the author proves the two-cardinal transfer theorem \((\kappa^{+},\kappa)\rightarrow (\kappa^{++},\kappa^{+})\). A key ingredient in the proof is the existence of a \((\kappa^{+}, 1)\)-coarse morass, which follows from \(V=L\).
MSC:
03C55 Set-theoretic model theory
03E05 Other combinatorial set theory
03E35 Consistency and independence results
03E45 Inner models, including constructibility, ordinal definability, and core models
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