Notre Dame Journal of Formal Logic

Models Omitting Given Complete Types

Akito Tsuboi

Abstract

We consider a problem of constructing a model that omits given complete types. We present two results. The first one is related to the Lopez-Escobar theorem and the second one is a version of Morley's omitting types theorem.

Article information

Source
Notre Dame J. Formal Logic, Volume 49, Number 4 (2008), 393-399.

Dates
First available in Project Euclid: 17 October 2008

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1224257538

Digital Object Identifier
doi:10.1215/00294527-2008-019

Mathematical Reviews number (MathSciNet)
MR2456655

Zentralblatt MATH identifier
1180.03037

Subjects
Primary: 03C50: Models with special properties (saturated, rigid, etc.) 03C52: Properties of classes of models

Keywords
omitting types Lopez-Escobar theorem Morley's theorem Hanf numbers

Citation

Tsuboi, Akito. Models Omitting Given Complete Types. Notre Dame J. Formal Logic 49 (2008), no. 4, 393--399. doi:10.1215/00294527-2008-019. https://projecteuclid.org/euclid.ndjfl/1224257538


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References

  • [1] Lopez-Escobar, E. G. K., ``An interpolation theorem for denumerably long formulas,'' Fundamenta Mathematicae, vol. 57 (1965), pp. 253--72.
  • [2] Newelski, L., "Omitting types and the real line", The Journal of Symbolic Logic, vol. 52 (1987), pp. 1020--1026.
  • [3] Shelah, S., "The Hanf number of omitting complete types", Pacific Journal of Mathematics, vol. 50 (1974), pp. 163--68.