Journal of Symbolic Logic

The two-cardinal problem for languages of arbitrary cardinality

Luis Miguel Villegas Silva

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Abstract

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

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

Dates
First available in Project Euclid: 9 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1278682200

Digital Object Identifier
doi:10.2178/jsl/1278682200

Mathematical Reviews number (MathSciNet)
MR2723767

Zentralblatt MATH identifier
1201.03018

Subjects
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

Keywords
Coarse morass cardinal transfer theorem two-cardinal problem

Citation

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. https://projecteuclid.org/euclid.jsl/1278682200


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