Transactions of the American Mathematical Society

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

 

 

A two-cardinal theorem for homogeneous sets and the elimination of Malitz quantifiers


Authors: Philipp Rothmaler and Peter Tuschik
Journal: Trans. Amer. Math. Soc. 269 (1982), 273-283
MSC: Primary 03C80; Secondary 03C10
MathSciNet review: 637038
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Sufficient conditions for the eliminability of Malitz quantifiers in a complete first order theory are given. Proving that certain superstable and not $ \omega $-stable theories satisfy these conditions, a question of Baldwin and Kueker is answered negatively.


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

  • [BK] John T. Baldwin and David W. Kueker, Ramsey quantifiers and the finite cover property, Pacific J. Math. 90 (1980), no. 1, 11–19. MR 599315
  • [FE] Solomon Feferman, Two notes on abstract model theory. II. Languages for which the set of valid sentences is semi-invariantly implicitly definable, Fund. Math. 89 (1975), no. 2, 111–130. MR 0491139
  • [GA] Steven Garavaglia, Relative strength of Malitz quantifiers, Notre Dame J. Formal Logic 19 (1978), no. 3, 495–503. MR 0485164
  • [MA] J. A. Makowsky, On some conjectures connected with complete sentences, Fund. Math. 81 (1974), 193–202. Collection of articles dedicated to Andrzej Mostowski on the occasion of his sixtieth birthday, III. MR 0366647
  • [MM] Menachem Magidor and Jerome Malitz, Compact extensions of 𝐿(𝑄). Ia, Ann. Math. Logic 11 (1977), no. 2, 217–261. MR 0453484
  • [SA] Gerald E. Sacks, Saturated model theory, W. A. Benjamin, Inc., Reading, Mass., 1972. Mathematics Lecture Note Series. MR 0398817
  • [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
  • [TU1] P. Tuschik, $ {\aleph _1}$-Kategorizität, Dissertation (A), Humboldt-Univ., Berlin, 1975.
  • [TU2] -, Elimination of cardinality quantifiers (contributed paper at the 4th Bierutowice Conf., Karpacz, Poland, September 1979).

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 03C80, 03C10

Retrieve articles in all journals with MSC: 03C80, 03C10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0637038-9
Keywords: Elimination of generalized quantifiers, first order theories, f.c.p., two cardinal theorem, stability, categoricity, finite axiomatizability
Article copyright: © Copyright 1982 American Mathematical Society