Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-22T17:38:24.323Z Has data issue: false hasContentIssue false
  • English
  • Français

Magidor-Malitz quantifiers in modules

Published online by Cambridge University Press:  12 March 2014

Andreas Baudisch
Andreas Baudisch*
Affiliation:
Institut für Mathematik, Akademie der Wissenschaften der Ddr, 1080 Berlin, DDR
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove the elimination of Magidor-Malitz quantifiers for R-modules relative to certain -core sentences and positive primitive formulas. For complete extensions of the elementary theory of R-modules it follows that all Ramsey quantifiers (ℵ0-interpretation) are eliminable. By a result of Baldwin and Kueker [1] this implies that there is no R-module having the finite cover property.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 49 , Issue 1 , March 1984 , pp. 1 - 8
Copyright
Copyright © Association for Symbolic Logic 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Baldwin, J. T. and Kueker, D. W., Ramsey quantifiers and the finite cover property, Pacific Journal of Mathematics, vol. 90 (1980), pp. 11–19.CrossRefGoogle Scholar
[2]Baudisch, A., Corrections and supplementaries to my paper concerning Abelian groups and the quantifier , Bulletin de l'Académie Polonaise des Sciences. Série des Sciences Mathématiques (to appear).Google Scholar
[3]Baur, W., ℵ0-categorical modules, this Journal, vol. 40 (1975), pp. 213–220.Google Scholar
[4]Baur, W., Elimination of quantifiers for modules, Israel Journal of Mathematics, vol. 25 (1976), pp. 64–70.CrossRefGoogle Scholar
[5]Eklof, P. C. and Sabbagh, G., Model-completions of modules, Annals of Mathematical Logic, vol. 2 (1971), pp. 251–295.CrossRefGoogle Scholar
[6]Fisher, E. R., Powers of saturated modules, this Journal, vol. 37 (1972), p. 777.Google Scholar
[7]Garavaglia, S., Direct product decompositions of theories of modules, this Journal, vol. 44 (1979), pp. 77–88.Google Scholar
[8]Keisler, H. J., Ultraproducts which are not saturated, this Journal, vol. 32 (1967), pp. 23–47.Google Scholar
[9]Magidor, M. and Malitz, J., Compact extensions of L(Q), Annals of Mathematical Logic, vol. 11 (1977), pp. 217–263.CrossRefGoogle Scholar
[10]Neumann, B. H., Groups covered by permutable cosets, Journal of the London Mathematical Society, vol. 29 (1954), pp. 236–248.CrossRefGoogle Scholar
[11]Rothmaler, P., Zur Modelltheorie der Moduln (unter besonderer Berücksichtigung der flachen Moduln), Dissertation A, Berlin, 1981.Google Scholar
[12]Shelah, S., Stability, the f.c.p., and superstability; model theoretic properties of formulas in first order theory, Annals of Mathematical Logic, vol. 3 (1971), pp. 271–362.CrossRefGoogle Scholar
[13]Wȩglorz, B., Equationally compact algebras (I), Fundamenta Mathematicae, vol. 59 (1966), pp. 289–298.CrossRefGoogle Scholar