ℳ-rank and meager groups

Ludomir Newelski

Fundamenta Mathematicae (1996)

  • Volume: 150, Issue: 2, page 149-171
  • ISSN: 0016-2736

Abstract

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Assume p* is a meager type in a superstable theory T. We investigate definability properties of p*-closure. We prove that if T has < 2 ℵ 0 countable models then the multiplicity rank ℳ of every type p is finite. We improve Saffe’s conjecture.

How to cite

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Newelski, Ludomir. "ℳ-rank and meager groups." Fundamenta Mathematicae 150.2 (1996): 149-171. <http://eudml.org/doc/212167>.

@article{Newelski1996,
abstract = {Assume p* is a meager type in a superstable theory T. We investigate definability properties of p*-closure. We prove that if T has $<2^\{ℵ_0\}$ countable models then the multiplicity rank ℳ of every type p is finite. We improve Saffe’s conjecture.},
author = {Newelski, Ludomir},
journal = {Fundamenta Mathematicae},
keywords = {meager group; superstable theory; definability; -closures; meager types; multiplicity rank},
language = {eng},
number = {2},
pages = {149-171},
title = {ℳ-rank and meager groups},
url = {http://eudml.org/doc/212167},
volume = {150},
year = {1996},
}

TY - JOUR
AU - Newelski, Ludomir
TI - ℳ-rank and meager groups
JO - Fundamenta Mathematicae
PY - 1996
VL - 150
IS - 2
SP - 149
EP - 171
AB - Assume p* is a meager type in a superstable theory T. We investigate definability properties of p*-closure. We prove that if T has $<2^{ℵ_0}$ countable models then the multiplicity rank ℳ of every type p is finite. We improve Saffe’s conjecture.
LA - eng
KW - meager group; superstable theory; definability; -closures; meager types; multiplicity rank
UR - http://eudml.org/doc/212167
ER -

References

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  1. [Ba] J. T. Baldwin, Fundamentals of Stability Theory, Springer, Berlin, 1988. 
  2. [Hru] E. Hrushovski, Locally modular regular types, in: Classification Theory, Proc., Chicago 1985, J. T. Baldwin (ed.), Springer, Berlin, 1988, 132-164. 
  3. [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. 
  4. [H-S] E. Hrushovski and S. Shelah, A dichotomy theorem for regular types, Ann. Pure Appl. Logic 45 (1989), 157-169. Zbl0697.03024
  5. [L-P] L. F. Low and A. Pillay, Superstable theories with few countable models, Arch. Math. Logic 31 (1992), 457-465. Zbl0806.03023
  6. [Ne1] L. Newelski, A model and its subset, J. Symbolic Logic 57 (1992), 644-658. Zbl0774.03015
  7. [Ne2] L. Newelski, Meager forking, Ann. Pure Appl. Logic 70 (1994), 141-175. Zbl0817.03017
  8. [Ne3] L. Newelski, ℳ-rank and meager types, Fund. Math. 146 (1995), 121-139. Zbl0829.03016
  9. [Ne4] L. Newelski, On atomic or saturated sets, J. Symbolic Logic, to appear. Zbl0863.03015
  10. [Ne5] L. Newelski, ℳ-gap conjecture and m-normal theories, preprint, 1995. 
  11. [Sh] S. Shelah, Classification Theory, 2nd ed., North-Holland, 1990. 
  12. [T] P. Tanovic, Fundamental order and the number of countable models, Ph.D. thesis, McGill University, December 1993. 

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