|
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  -stable theories satisfy these conditions, a question of Baldwin and Kueker is answered negatively.
- [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
(83e:03054)
- [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
(58 #10405)
- [GA]
Steven
Garavaglia, Relative strength of Malitz quantifiers, Notre
Dame J. Formal Logic 19 (1978), no. 3, 495–503.
MR
0485164 (58 #5018)
- [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
(51 #2894)
- [MM]
Menachem
Magidor and Jerome
Malitz, Compact extensions of 𝐿(𝑄). Ia, Ann.
Math. Logic 11 (1977), no. 2, 217–261. MR 0453484
(56 #11746)
- [SA]
Gerald
E. Sacks, Saturated model theory, W. A. Benjamin, Inc.,
Reading, Mass., 1972. Mathematics Lecture Note Series. MR 0398817
(53 #2668)
- [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, 1978. MR 513226
(81a:03030)
- [TU1]
P. Tuschik,
 -Kategorizität, Dissertation (A), Humboldt-Univ., Berlin, 1975.
- [TU2]
-, Elimination of cardinality quantifiers (contributed paper at the 4th Bierutowice Conf., Karpacz, Poland, September 1979).
- [BK]
- J. T. Baldwin and D. W. Kueker, Ramsey quantifiers and the finite cover property, Pacific J. Math. 90 (1980), 11-19. MR 599315 (83e:03054)
- [FE]
- S. Feferman, Two notes on abstract model theory. II, Fund. Math. 89 (1975), 111-130. MR 0491139 (58:10405)
- [GA]
- S. Garavaglia, Relative strength of Malitz quantifiers (preprint). MR 0485164 (58:5018)
- [MA]
- J. A. Makowsky, On some conjectures connected with complete sentences, Fund. Math. 81 (1974), 193-202. MR 0366647 (51:2894)
- [MM]
- M. Magidor and J. Malitz, Compact extensions of
 , Ann. Math. Logic 11 (1977), 217-261. MR 0453484 (56:11746)
- [SA]
- G. E. Sacks, Saturated model theory, Benjamin, New York, 1972. MR 0398817 (53:2668)
- [SH]
- S. Shelah, Classification theory and the number of non-isomorphic models, North-Holland, Amsterdam, 1978. MR 513226 (81a:03030)
- [TU1]
- P. Tuschik, -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
PII:
S 0002-9947(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
|
