On $U$-rank $2$ types
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- by Ludomir Newelski PDF
- Trans. Amer. Math. Soc. 344 (1994), 553-581 Request permission
Abstract:
Let T be a superstable theory with $< {2^{{\aleph _0}}}$ countable models. We study some special types $p \in S(\emptyset )$ of U-rank 2 called skeletal (cf. [Bu4]). We reduce an eventual version of the problem of counting isomorphism types of sets $p(M)$ for countable M to a problem from linear algebra.References
- John T. Baldwin, Fundamentals of stability theory, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1988. MR 918762, DOI 10.1007/978-3-662-07330-8
- Steven Buechler, The geometry of weakly minimal types, J. Symbolic Logic 50 (1985), no. 4, 1044–1053 (1986). MR 820131, DOI 10.2307/2273989
- Steven Buechler, The classification of small weakly minimal sets. I, Classification theory (Chicago, IL, 1985) Lecture Notes in Math., vol. 1292, Springer, Berlin, 1987, pp. 32–71. MR 1033022, DOI 10.1007/BFb0082231 —, Classification of small weakly minimal sets III 1/2, manuscript. —, Rank 2 types vis-a-vis Vaught’s conjecture, preprint, 1989. —, Vaught’s conjecture for unidimensional theories. I: The tree theorem, preprint, 1991. S. Buechler and L. Newelski, On the geometry of U-rank 2 types, Logic Colloquium ’90 (submitted).
- G. Cherlin, L. Harrington, and A. H. Lachlan, $\aleph _0$-categorical, $\aleph _0$-stable structures, Ann. Pure Appl. Logic 28 (1985), no. 2, 103–135. MR 779159, DOI 10.1016/0168-0072(85)90023-5
- Vlastimil Dlab and Claus Michael Ringel, On algebras of finite representation type, J. Algebra 33 (1975), 306–394. MR 357506, DOI 10.1016/0021-8693(75)90125-8
- Ehud Hrushovski, Locally modular regular types, Classification theory (Chicago, IL, 1985) Lecture Notes in Math., vol. 1292, Springer, Berlin, 1987, pp. 132–164. MR 1033027, DOI 10.1007/BFb0082236
- Ludomir Newelski, A proof of Saffe’s conjecture, Fund. Math. 134 (1990), no. 2, 143–155. MR 1074641, DOI 10.4064/fm-134-2-143-155
- Ludomir Newelski, Weakly minimal formulas: a global approach, Ann. Pure Appl. Logic 46 (1990), no. 1, 65–94. MR 1040387, DOI 10.1016/0168-0072(90)90078-G —, Classifying U-rank 2 types, manuscript, February 1989. A. Pillay, Geometrical stability theory (in preparation).
- 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
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 344 (1994), 553-581
- MSC: Primary 03C45
- DOI: https://doi.org/10.1090/S0002-9947-1994-1142779-1
- MathSciNet review: 1142779