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  • Donald W. Barnes
  • John M. Mack
Part of the Graduate Texts in Mathematics book series (GTM, volume 22)

Abstract

In many branches of mathematics, where one is studying a system of some particular type, it is of interest to find out ways of forming new systems of the given type from known examples. One useful method that can often be applied is based on the cartesian product construction. In this section we investigate this construction in the case where the underlying system is a first-order theory T = (, A, C), and (M i , v i , ψ i ) for iI is a family of models of T. We therefore investigate the possibility of making
$$ M = \prod\nolimits_{i \in I} {{M_i}} $$
into a model of T, independently of the particular nature of T.

Keywords

Direct Limit Countable Model Monic Polynomial Congruence Class Inaccessible Cardinal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1975

Authors and Affiliations

  • Donald W. Barnes
    • 1
  • John M. Mack
    • 1
  1. 1.Department of Pure MathematicsThe University of SydneySydneyAustralia

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