"Gap 1" two-cardinal principles and the omitting types theorem for ℒ(Q)

S. Shelah

doi:10.1007/BF02764857

"Gap 1" two-cardinal principles and the omitting types theorem for ℒ(Q)

S. Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

For λ a strong limit singular cardinal, and more generally for λ > 2^{cof λ}, we prove the equivalence of a number of model theoretic and combinatorial conditions, including the ℒ(Q)-completeness theorem for the λ⁺-interpretation, an omitting types theorem for ℒ(Q) in the λ⁺-interpretation, and a weak form of Jensen's principle □_λ.

Original language	English
Pages (from-to)	133-152
Number of pages	20
Journal	Israel Journal of Mathematics
Volume	65
Issue number	2
DOIs	https://doi.org/10.1007/BF02764857
State	Published - Jun 1989

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10.1007/BF02764857

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abstract = "For λ a strong limit singular cardinal, and more generally for λ > 2cof λ, we prove the equivalence of a number of model theoretic and combinatorial conditions, including the ℒ(Q)-completeness theorem for the λ +-interpretation, an omitting types theorem for ℒ(Q) in the λ +-interpretation, and a weak form of Jensen's principle □λ.",

author = "S. Shelah",

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AB - For λ a strong limit singular cardinal, and more generally for λ > 2cof λ, we prove the equivalence of a number of model theoretic and combinatorial conditions, including the ℒ(Q)-completeness theorem for the λ +-interpretation, an omitting types theorem for ℒ(Q) in the λ +-interpretation, and a weak form of Jensen's principle □λ.

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JO - Israel Journal of Mathematics

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IS - 2

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"Gap 1" two-cardinal principles and the omitting types theorem for ℒ(Q)

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