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A gap 1 cardinal transfer theorem. (English) Zbl 1095.03051
Summary: We extend the gap 1 cardinal transfer theorem \((\kappa^+,\kappa) \to (\lambda^+,\lambda)\) to any language of cardinality \(\leq \lambda\), where \(\lambda\) is a regular cardinal. This transfer theorem has been proved by Chang under GCH for countable languages and by Silver in some cases for bigger languages (also under GCH). We assume the existence of a coarse \((\lambda, 1)\)-morass instead of GCH.

MSC:
03E45 Inner models, including constructibility, ordinal definability, and core models
03C55 Set-theoretic model theory
03E05 Other combinatorial set theory
03C80 Logic with extra quantifiers and operators
03C50 Models with special properties (saturated, rigid, etc.)
03E35 Consistency and independence results
03E65 Other set-theoretic hypotheses and axioms
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