# zbMATH — the first resource for mathematics

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
Full Text:
##### References:
 [1] Coarse morasses in L 872 (1981) · Zbl 0476.03049 [2] Constructibility (1984) · Zbl 0542.03029 [3] Model theory (1993) [4] DOI: 10.1090/S0002-9939-1965-0193016-3 [5] Model theory (1993) [6] On regular reduced products 67 pp 1169– (2002) [7] Axiomatic set theory 13 pp 143– (1971) [8] DOI: 10.1016/0003-4843(72)90001-0 · Zbl 0257.02035 [9] DOI: 10.1002/malq.200510038 · Zbl 1095.03051
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.