Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-24T07:49:36.427Z Has data issue: false hasContentIssue false
  • English
  • Français

Undecidable Lt theories of topological abelian groups

Published online by Cambridge University Press:  12 March 2014

Gregory L. Cherlin  and
Peter H. Schmitt
Gregory L. Cherlin
Affiliation:
Rutgers, The State University, New Brunswick, New Jersey 08903
Peter H. Schmitt
Affiliation:
University of Heidelberg, Heidelberg, Federal Republic of Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove the hereditary undecidability of the Lt theories of:

(1) torsion-free Hausdorff topological abelian groups;

(2) locally pure Hausdorff topological abelian groups.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 46 , Issue 4 , December 1981 , pp. 761 - 772
Copyright
Copyright © Association for Symbolic Logic 1981

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]Baudisch, A., Decidability of the theory of abelian groups with a predicate for pure subgroup (to appear).Google Scholar
[2]Baur, W., Undecidability of the theory of abelian groups with a subgroup, Proceedings of the American Mathematical Society, vol. 55 (1976), pp. 125–128.CrossRefGoogle Scholar
[3]Cherlin, G. and Schmitt, P. H., Decidable Lt-theories of topological abelian groups (to appear).Google Scholar
[4]Davis, M., Computability and unsoU ability, McGraw-Hill, New York, 1958.Google Scholar
[5]Eklof, P. C. and Fisher, E. R., The elementary theory of abelian groups, Annals of Mathematical Logic, vol. 4 (1972), pp. 115–171.CrossRefGoogle Scholar
[6]Flum, J. and Ziegler, M.Topological model theory, Lecture Notes in Mathematics, No. 769, Springer-Verlag, New York, 1980.Google Scholar
[7]Fuchs, L., Infinite abelian groups. I, II, Academic Press, New York, 1970, 1973.Google Scholar
[8]Garavaglia, S., Model theory of topological structures, Annals of Mathematical Logic, vol. 14 (1978), pp. 13–37.CrossRefGoogle Scholar
[9]Gurevitch, Y., Elementary properties of ordered abelian groups, Translations of the American Mathematical Society, vol. 46 (1965), pp. 165–192.Google Scholar
[10]Kokorin, A. I. and Kozlow, G. T., Elementary theory of abelian groups without torsion with apredicate A selecting a subgroup, Algebra and Logic, vol. 8 (1969), pp. 182–198.Google Scholar
[11]Kokorin, A. I. and Kozlow, G. T., Proof of a lemma on model completeness (Correction to [10]), Algebra and Logic, vol. 14 (1975), pp. 328–330.Google Scholar
[12]Mart'yanov, V. I., The theory of abelian groups with predicates specifying a subgroup and with endomorphism operations, Algebra and Logic, vol. 14 (1975), pp. 330–334.CrossRefGoogle Scholar
[13]McKee, T. A., Infinitary logic and topological homeomorphisms, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 21 (1975), pp. 405–408.CrossRefGoogle Scholar
[14]McKee, T. A., Sentences preserved between equivalent topological bases, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 22 (1976), pp. 79–84.CrossRefGoogle Scholar
[15]Slobodskoi, A. M. and Fridman, E. I., Theories of abelian groups wth predicates specifying a subgroup, Algebra and Logic, vol. 14 (1975), pp. 353–355.CrossRefGoogle Scholar
[16]Szmielew, W., Elementary properties of abelian groups, Fundamenta Mathematical, vol. 41 (1955), pp. 203–271.CrossRefGoogle Scholar
[17]Ziegler, M., A language for topological structures which satisfies a Lindström theorem, Bulletin of the American Mathematical Society, vol. 82 (1976), pp. 568–570.CrossRefGoogle Scholar