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Downward transfer of satisfiability for sentences of L1,1

Published online by Cambridge University Press:  12 March 2014

Jerome Malitz
Jerome Malitz*
Affiliation:
University of Colorado, Boulder, Colorado 80309
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Abstract

The quantifier Qm,n binds m + n variables. In the κ-interpretation M ⊨ means that there is a κ-powered proper subset X of ∣M∣ such that whenever ā ∈ mX and then M ⊨ ϕā, . If σ ∈ Lm, n has a model in the κ-interpretation does it have a model in the λ-interpretation? For σ ∈ L1, 1, κ regular and uncountable, and λ = ω1 the answer is yes.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 48 , Issue 4 , December 1983 , pp. 1146 - 1150
Copyright
Copyright © Association for Symbolic Logic 1983

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References

REFERENCES

[K]Keisler, H.J., Logic with the quantifier “there exist uncountably many”, Annals of Mathematical Logic, vol. 1 (1970), pp. 1–94.CrossRefGoogle Scholar
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[S]Shelah, S., Models of second-order properties. III: Omitting types for L(Q), Archiv für Mathematische Logik und Grundlagenforschung, vol. 21 (1980), pp. 1–11.CrossRefGoogle Scholar