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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On residual properties


Author: Alan H. Mekler
Journal: Proc. Amer. Math. Soc. 78 (1980), 187-188
MSC: Primary 03C52; Secondary 03C60, 20A15
DOI: https://doi.org/10.1090/S0002-9939-1980-0550490-6
MathSciNet review: 550490
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Abstract: It is shown that the class of structures residually in a universal class closed under elementary equivalence is definable by a sentence of $ {L_{\infty \omega }}$.


References [Enhancements On Off] (What's this?)

  • [1] C. C. Chang and H. J. Keisler, Model theory, North-Holland, Amsterdam, 1973.
  • [2] B. H. Neumann, Properties of countable character, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 293–296. MR 0480286
  • [3] B. H. Neumann, Group properties of countable character, Selected questions of algebra and logic (collection dedicated to the memory of A. I. Mal′cev)(Russian), Izdat. “Nauka” Sibirsk. Otdel., Novosibirsk, 1973, pp. 197–204. MR 0327912
  • [4] Gabriel Sabbagh, On properties of countable character, Bull. Austral. Math. Soc. 4 (1971), 183–192. MR 0281677, https://doi.org/10.1017/S000497270004644X

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0550490-6
Article copyright: © Copyright 1980 American Mathematical Society