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Elementary theories of complete torsion-free Abelian groups with p-ary topology

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Abstract

The complete torsion-free Abelian groups are investigated as dibasic RPC models whose second basic set comprises subgroups forming a chain with factors of order p. Two theorems about the elementary theories of classes of such models are proved.

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Literature cited

  1. Yu. L. Ershov, “New examples of undecidable theories,” Algebra i Logika,5, No. 5, 37–47 (1966).

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  2. I. A. Lavrov, “The effective inseparability of the set of identically true formulas and the set of finitely refutable formulas for certain elementary theories,” Algebra i Logika,2, No. 1, 5–18 (1963).

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  3. M. A. Taitslin, Theory of Models [in Russian], Novosibirsk (1970).

  4. K. Kuratovskii and A. Mostovskii, Set Theory [in Russian], Moscow (1970).

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Authors
  1. É. S. Vasil'ev
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Additional information

Translated from Matematicheskie Zametki, Vol. 14, No. 2, pp. 201–208, August, 1973.

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Vasil'ev, É.S. Elementary theories of complete torsion-free Abelian groups with p-ary topology. Mathematical Notes of the Academy of Sciences of the USSR 14, 673–677 (1973). https://doi.org/10.1007/BF01147112

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  • DOI: https://doi.org/10.1007/BF01147112

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