Weakly definable types

Kirby, L. A. S.; Pillay, A.

doi:10.1090/S0002-9947-1986-0833696-8

Weakly definable types
HTML articles powered by AMS MathViewer

by L. A. S. Kirby and A. Pillay PDF

Trans. Amer. Math. Soc. 295 (1986), 547-563 Request permission

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

Haim Gaifman, Models and types of Peano’s arithmetic, Ann. Math. Logic 9 (1976), no. 3, 223–306. MR 406791, DOI 10.1016/0003-4843(76)90002-4
L. A. S. Kirby, Ultrafilters and types on models of arithmetic, Ann. Pure Appl. Logic 27 (1984), no. 3, 215–252. MR 765591, DOI 10.1016/0168-0072(84)90027-7
Daniel Lascar, Ranks and definability in superstable theories, Israel J. Math. 23 (1976), no. 1, 53–87. MR 409169, DOI 10.1007/BF02757234
Daniel Lascar and Bruno Poizat, An introduction to forking, J. Symbolic Logic 44 (1979), no. 3, 330–350. MR 540665, DOI 10.2307/2273127
Per Lindström, Remarks on some theorems of Keisler, J. Symbolic Logic 33 (1968), 571–576. MR 269493, DOI 10.2307/2271366
Anand Pillay, An introduction to stability theory, Oxford Logic Guides, vol. 8, The Clarendon Press, Oxford University Press, New York, 1983. MR 719195
Bruno Poizat, Sous-groupes définissables d’un groupe stable, J. Symbolic Logic 46 (1981), no. 1, 137–146 (French). MR 604887, DOI 10.2307/2273265

48

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

An unstable

categorical theory without the strict order property