Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Amalgamation and elimination of quantifiers for theories of fields


Author: William H. Wheeler
Journal: Proc. Amer. Math. Soc. 77 (1979), 243-250
MSC: Primary 03C60; Secondary 12L99
DOI: https://doi.org/10.1090/S0002-9939-1979-0542092-4
MathSciNet review: 542092
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The universal theories of integral domains and of ordered integral domains which have the amalgamation property are characterized via their existentially complete models. The results of A. Macintyre, K. McKenna, and L. van den Dries on fields and ordered fields whose complete theories permit elimination of quantifiers are then derived as easy corollaries.


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

  • [1] P. Bacsich, Amalgamation properties and interpolation theorems for equational theories, Algebra Universalis 5 (1975), 45-55. MR 0381984 (52:2873)
  • [2] G. Cherlin, Model theoretic algebra-selected topics, Lecture Notes in Math., vol. 521, Springer-Verlag, Berlin, 1976. MR 0539999 (58:27455)
  • [3] J. Hirschfeld and W. H. Wheeler, Forcing, arithmetic, division rings, Lecture Notes in Math., vol. 454, Springer-Verlag, Berlin, 1975. MR 0389581 (52:10412)
  • [4] A. Macintyre, On $ {\omega _1}$-categorical theories of fields, Fund. Math. 71 (1971), 1-25. MR 0290954 (45:48)
  • [5] A. Macintyre, K. McKenna and L. P. D. van den Dries, Elimination of quantifiers in algebraic structures (to appear).
  • [6] B. Rose, Rings which admit elimination of quantifiers, J. Symbolic Logic 43 (1978), 92-112. MR 495121 (80e:03036a)
  • [7] G. Sacks, Saturated model theory, W. A. Benjamin, Inc., Reading, Mass., 1972. MR 0398817 (53:2668)
  • [8] J. R. Shoenfield, Mathematical logic, Addison-Wesley Publishing Co., Reading, Mass., 1967. MR 0225631 (37:1224)
  • [9] L. P. D. van den Dries, Model theory of fields, Dissertation, Utrecht, 1978.
  • [10] W. H. Wheeler, Amalgamation, elimination of quantifiers, and theories of fields, Abstract, J. Symbolic Logic (to appear). MR 542092 (80j:03049)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03C60, 12L99

Retrieve articles in all journals with MSC: 03C60, 12L99


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0542092-4
Keywords: Theories of fields, elimination of quantifiers, amalgamation, algebraically closed fields, real closed order fields
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society