No abstract

The article gives an overview of the development of model theory in Kazakhstan over the past 60 years from the standpoint of the tasks that stood at that time. We consider directions that naturally arose from the definition of truth in a model and under the influence of Doctor of Physical and Mathematical Sciences, Academician A. Taimanov, initiator of the growth of model theory in Kazakhstan.

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We present a method for constructing countable models of small theories and apply it to prove theorems on the maximal number of countable non-isomorphic models of linearly ordered theories.