Journal of Symbolic Logic

End Extensions and Numbers of Countable Models

Saharon Shelah

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Abstract

We prove that every model of $T = \mathrm{Th}(\omega, <, \ldots) (T$ countable) has an end extension; and that every countable theory with an infinite order and Skolem functions has $2^{\mathbf{\aleph}_0}$ nonisomorphic countable models; and that if every model of $T$ has an end extension, then every $|T|$-universal model of $T$ has an end extension definable with parameters.

Article information

Source
J. Symbolic Logic, Volume 43, Issue 3 (1978), 550-562.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183740260

Mathematical Reviews number (MathSciNet)
MR503792

Zentralblatt MATH identifier
0412.03043

JSTOR
links.jstor.org

Citation

Shelah, Saharon. End Extensions and Numbers of Countable Models. J. Symbolic Logic 43 (1978), no. 3, 550--562. https://projecteuclid.org/euclid.jsl/1183740260


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