Abstract
AssumeG is a superstable group ofM-rank 1 and the division ring of pseudo-endomorphisms ofG is a prime field. We prove a relative Vaught’s conjecture for Th(G). When additionallyU(G) =ω, this yields Vaught’s conjecture for Th(G).
Similar content being viewed by others
References
J. T. Baldwin,Fundamentals of Stability Theory, Springer, Berlin, 1988.
S. Buechler,Classification of small w.m. sets, I, inClassification Theory, Proceedings, Chicago 1985 (J. T. Baldwin, ed.), Springer, Berlin, 1987, pp. 32–71.
S. Buechler,Vaught’s conjecture for superstable theories of finite rank, Annals of Pure and Applied Logic, to appear.
E. Hrushovski,Locally modular regular types, inClassification Theory, Proceedings, Chicago 1985 (J. T. Baldwin, ed.), Springer, Berlin, 1987, pp. 132–164.
E. Hrushovski and A. Pillay,Weakly normal groups, inLogic Colloquium 1985 (The Paris Logic Group, ed.), North-Holland, Amsterdam, 1987, pp. 233–244.
E. Hrushovski and S. Shelah,A dichotomy theorem for regular types, Annals of Pure and Applied Logic45 (1989), 157–169.
J. Loveys,Abelian groups with modular generics, Journal of Symbolic Logic56 (1991), 250–259.
M. Makkai,A survey of basic stability theory, with particular emphasis on orthogonality and regular types, Israel Journal of Mathematics49 (1984), 181–238.
L. Newelski,A proof of Saffe’s conjecture, Fundamenta Mathematicae134 (1990), 143–155.
L. Newelski,A model and its subset, Journal of Symbolic Logic57 (1992), 644–658.
L. Newelski,Scott analysis of pseudo-types, Journal of Symbolic Logic58 (1993), 648–663.
L. Newelski,Meager forking, Annals of Pure and Applied Logic70 (1994), 141–175.
L. Newelski,M-rank and meager types, Fundamenta Mathematicae146 (1995), 121–139.
L. Newelski,M-rank and meager groups, Fundamenta Mathematicae150 (1996), 149–171.
L. Newelski,M-gap conjecture and m-normal theories, Israel Journal of Mathematics106 (1998), 285–311.
A. Pillay,Certain locally modular regular superstable groups, preprint 1992.
S. Shelah, L. Harrington and M. Makkai,A proof of Vaught’s conjecture for ℵ 0-stable theories, Israel Journal of Mathematics49 (1984), 259–278.
S. Shelah,Classification Theory, 2nd edn., North-Holland, Amsterdam, 1990.
Author information
Authors and Affiliations
Corresponding author
Additional information
Research supported by KBN grant 2 P03A 006 09.
Rights and permissions
About this article
Cite this article
Newelski, L. Vaught’s conjecture for some meager groups. Isr. J. Math. 112, 271–299 (1999). https://doi.org/10.1007/BF02773485
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02773485