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2014 Dependent $T$ and existence of limit models
Saharon Shelah
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Tbilisi Math. J. 7(1): 99-128 (2014). DOI: 10.2478/tmj-2014-0010


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.


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Saharon Shelah. "Dependent $T$ and existence of limit models." Tbilisi Math. J. 7 (1) 99 - 128, 2014.


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

zbMATH: 1335.03033
MathSciNet: MR3313049
Digital Object Identifier: 10.2478/tmj-2014-0010

Primary: 03C45
Secondary: 03C55 , 06A05

Keywords: Classification theory , dependent theories , limit models , linear order , model theory

Rights: Copyright © 2014 Tbilisi Centre for Mathematical Sciences

Vol.7 • No. 1 • 2014
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