Journal of Symbolic Logic

The two-cardinal problem for languages of arbitrary cardinality

Luis Miguel Villegas Silva

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Let ℒ be a first-order language of cardinality κ++ with a distinguished unary predicate symbol U. In this paper we prove, working on L, the two cardinal transfer theorem (κ⁺,κ) ⇒ (κ++,κ⁺) for this language. This problem was posed by Chang and Keisler more than twenty years ago.

Article information

J. Symbolic Logic, Volume 75, Issue 3 (2010), 785-801.

First available in Project Euclid: 9 July 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03C55: Set-theoretic model theory 03C80: Logic with extra quantifiers and operators [See also 03B42, 03B44, 03B45, 03B48] 03E05: Other combinatorial set theory 03E45: Inner models, including constructibility, ordinal definability, and core models
Secondary: 03C50: Models with special properties (saturated, rigid, etc.) 03E35: Consistency and independence results 03E65: Other hypotheses and axioms

Coarse morass cardinal transfer theorem two-cardinal problem


Villegas Silva, Luis Miguel. The two-cardinal problem for languages of arbitrary cardinality. J. Symbolic Logic 75 (2010), no. 3, 785--801. doi:10.2178/jsl/1278682200.

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