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Omitting types in incomplete theories

Published online by Cambridge University Press:  12 March 2014

Enrique Casanovas  and
Rafel Farré
Enrique Casanovas
Affiliation:
Dep. de Lògica, Hist. i Fil. de la Ciència, Universitat de Barcelona, Baldiri Reixac s/n, 08028 Barcelona, Spain, E-mail: casanova@cerber.mat.ub.es
Rafel Farré
Affiliation:
Dep. de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Pau Gargallo, 5, 08028 Barcelona, Spain, E-mail: farre@ma2.upc.es
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Abstract

We characterize omissibility of a type, or a family of types, in a countable theory in terms of non-existence of a certain tree of formulas. We extend results of L. Newelski on omitting < covK non-isolated types. As a consequence we prove that omissibility of a family of < covK types is equivalent to omissibility of each countable subfamily.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 1 , March 1996 , pp. 236 - 245
Copyright
Copyright © Association for Symbolic Logic 1996

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References

REFERENCES

[1]Newelski, Ludomir, Omitting types and the real line, this Journal, vol. 52 (1987), pp. 1020–1026.Google Scholar
[2]Newelski, Ludomir, Omitting types for stable ccc theories, this Journal, vol. 55 (1990), pp. 1037–1047.Google Scholar
[3]Shelah, Saharon, Classification theory, second ed., North Holland P.C., Amsterdam, 1990.Google Scholar
[4]Simmons, Harold, An omitting types theorem with an application to the construction of generic structures, Mathematica Scandinavica, vol. 33 (1973), pp. 46–54.CrossRefGoogle Scholar