Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Weakly definable types


Authors: L. A. S. Kirby and A. Pillay
Journal: Trans. Amer. Math. Soc. 295 (1986), 547-563
MSC: Primary 03C45; Secondary 03C40, 03G05, 03H15
MathSciNet review: 833696
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study some generalizations of the notion of a definable type, first in an abstract setting in terms of ultrafilters on certain Boolean algebras, and then as applied to model theory.


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

  • [G] Haim Gaifman, Models and types of Peano’s arithmetic, Ann. Math. Logic 9 (1976), no. 3, 223–306. MR 0406791
  • [K] L. A. S. Kirby, Ultrafilters and types on models of arithmetic, Ann. Pure Appl. Logic 27 (1984), no. 3, 215–252. MR 765591, 10.1016/0168-0072(84)90027-7
  • [L] Daniel Lascar, Ranks and definability in superstable theories, Israel J. Math. 23 (1976), no. 1, 53–87. MR 0409169
  • [LP] Daniel Lascar and Bruno Poizat, An introduction to forking, J. Symbolic Logic 44 (1979), no. 3, 330–350. MR 540665, 10.2307/2273127
  • [Li] Per Lindström, Remarks on some theorems of Keisler, J. Symbolic Logic 33 (1968), 571–576. MR 0269493
  • [Pi] Anand Pillay, An introduction to stability theory, Oxford Logic Guides, vol. 8, The Clarendon Press, Oxford University Press, New York, 1983. MR 719195
  • [P] Bruno Poizat, Sous-groupes définissables d’un groupe stable, J. Symbolic Logic 46 (1981), no. 1, 137–146 (French). MR 604887, 10.2307/2273265
  • [R] J. P. Ressayre, Review in J. Symbolic Logic 48 (1983), 484-485.
  • [Sh] Saharon Shelah, Classification theory and the number of nonisomorphic models, Studies in Logic and the Foundations of Mathematics, vol. 92, North-Holland Publishing Co., Amsterdam-New York, 1978. MR 513226
  • [TW] H. P. Tuschik and M. Weese, An unstable $ {\aleph _0}$-categorical theory without the strict order property, Proc. 1st Easter Conf. on Model Theory (Diedrichshagen, DDR, 1983), Humboldt-Universität zu Berlin, 1983.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 03C45, 03C40, 03G05, 03H15

Retrieve articles in all journals with MSC: 03C45, 03C40, 03G05, 03H15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0833696-8
Article copyright: © Copyright 1986 American Mathematical Society