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On the independence property of first order theories and indiscernible sequences

Abstract

We refute the strong version of Shelah’s conjecture about models of large cardinalities, the independence property, and indiscernible sequences. We find necessary and sufficient conditions for a theory to lack the independence property and present applications of these conditions.

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Correspondence to K. Zh. Kudaĭbergenov.

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Original Russian Text © K. Zh. Kudaĭbergenov, 2011, published in Matematicheskie Trudy, 2011, Vol. 14, No. 1, pp. 126–140.

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Kudaĭbergenov, K.Z. On the independence property of first order theories and indiscernible sequences. Sib. Adv. Math. 21, 282–291 (2011). https://doi.org/10.3103/S1055134411040067

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Keywords

  • the independence property
  • indiscernible sequence
  • the theory of a linearly ordered set
  • the theory of a tree