Assume p* is a meager type in a superstable theory T. We investigate definability properties of p*-closure. We prove that if T has countable models then the multiplicity rank ℳ of every type p is finite. We improve Saffe’s conjecture.
@article{bwmeta1.element.bwnjournal-article-fmv150i2p149bwm,
author = {Ludomir Newelski},
title = {M-rank and meager groups},
journal = {Fundamenta Mathematicae},
volume = {149},
year = {1996},
pages = {149-171},
zbl = {0865.03022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv150i2p149bwm}
}
Newelski, Ludomir. ℳ-rank and meager groups. Fundamenta Mathematicae, Tome 149 (1996) pp. 149-171. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv150i2p149bwm/
[00000] [Ba] J. T. Baldwin, Fundamentals of Stability Theory, Springer, Berlin, 1988.
[00001] [Hru] E. Hrushovski, Locally modular regular types, in: Classification Theory, Proc., Chicago 1985, J. T. Baldwin (ed.), Springer, Berlin, 1988, 132-164.
[00002] [H-P] E. Hrushovski and A. Pillay, Weakly normal groups, in: Logic Colloquium '85, The Paris Logic Group (eds.), North-Holland, Amsterdam, 1987, 233-244.
[00003] [H-S] E. Hrushovski and S. Shelah, A dichotomy theorem for regular types, Ann. Pure Appl. Logic 45 (1989), 157-169. | Zbl 0697.03024
[00004] [L-P] L. F. Low and A. Pillay, Superstable theories with few countable models, Arch. Math. Logic 31 (1992), 457-465. | Zbl 0806.03023
[00005] [Ne1] L. Newelski, A model and its subset, J. Symbolic Logic 57 (1992), 644-658. | Zbl 0774.03015
[00006] [Ne2] L. Newelski, Meager forking, Ann. Pure Appl. Logic 70 (1994), 141-175. | Zbl 0817.03017
[00007] [Ne3] L. Newelski, ℳ-rank and meager types, Fund. Math. 146 (1995), 121-139. | Zbl 0829.03016
[00008] [Ne4] L. Newelski, On atomic or saturated sets, J. Symbolic Logic, to appear. | Zbl 0863.03015
[00009] [Ne5] L. Newelski, ℳ-gap conjecture and m-normal theories, preprint, 1995.
[00010] [Sh] S. Shelah, Classification Theory, 2nd ed., North-Holland, 1990.
[00011] [T] P. Tanovic, Fundamental order and the number of countable models, Ph.D. thesis, McGill University, December 1993.