Tbilisi Mathematical Journal

Dependent $T$ and existence of limit models

Saharon Shelah

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Abstract

Does the class of linear orders have (one of the variants of) the so called $(\lambda,\kappa)$-limit model? It is necessarily unique, and naturally assuming some instances of G.C.H. we get some positive results. More generally, letting $T$ be a complete first order theory and for simplicity assume G.C.H., for regular $\lambda > \kappa > |T|$ does $T$ have (variants of) a $(\lambda,\kappa)$-limit models, except for stable $T$? For some, yes, the theory of dense linear order, for some, no. Moreover, for independent $T$ we get negative results. We deal more with linear orders.

Article information

Source
Tbilisi Math. J., Volume 7, Issue 1 (2014), 99-128.

Dates
Received: 29 September 2009
Accepted: 20 November 2014
First available in Project Euclid: 12 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528768956

Digital Object Identifier
doi:10.2478/tmj-2014-0010

Mathematical Reviews number (MathSciNet)
MR3313049

Zentralblatt MATH identifier
1335.03033

Subjects
Primary: 03C45: Classification theory, stability and related concepts [See also 03C48]
Secondary: 03C55: Set-theoretic model theory 06A05: Total order

Keywords
Model theory classification theory dependent theories limit models linear order

Citation

Shelah, Saharon. Dependent $T$ and existence of limit models. Tbilisi Math. J. 7 (2014), no. 1, 99--128. doi:10.2478/tmj-2014-0010. https://projecteuclid.org/euclid.tbilisi/1528768956


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