Journal of Symbolic Logic

Weak Definability in Infinitary Languages

Saharon Shelah

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Abstract

We shall prove that if a model of cardinality $\kappa$ can be expanded to a model of a sentence $\psi$ of $L_{\lambda^+,\omega}$ by adding a suitable predicate in more than $\kappa$ ways, then, it has a submodel of power $\mu$ which can be expanded to a model of $\psi$ in $> \mu$ ways provided that $\lambda,\kappa,\mu$ satisfy suitable conditions.

Article information

Source
J. Symbolic Logic, Volume 38, Issue 3 (1973), 399-404.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183738749

Mathematical Reviews number (MathSciNet)
MR369027

Zentralblatt MATH identifier
0284.02027

JSTOR
links.jstor.org

Citation

Shelah, Saharon. Weak Definability in Infinitary Languages. J. Symbolic Logic 38 (1973), no. 3, 399--404. https://projecteuclid.org/euclid.jsl/1183738749


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