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1
Content available remote

m-normal theories

100%
Newelski L.
Fundamenta Mathematicae
|
2001
|
tom 170
|
nr 1-2
141-163
EN
Originally, m-independence, ℳ -rank, m-stability and m-normality were defined only for small stable theories. Here we extend the definitions to an arbitrary small countable complete theory. Then we investigate these notions in the new, broader context. As a consequence we show that any superstable theory with $< 2^{ℵ₀}$ countable models is m-normal. In particular, any *-algebraic group interpretable in such a theory is abelian-by-finite.
2
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ℳ-rank and meager groups

100%
Newelski L.
Fundamenta Mathematicae
|
1996
|
tom 150
|
nr 2
149-171
EN
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.
3
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ℳ-rank and meager types

100%
Newelski L.
Fundamenta Mathematicae
|
1994-1995
|
tom 146
|
nr 2
121-139
EN
Assume T is superstable and small. Using the multiplicity rank ℳ we find locally modular types in the same manner as U-rank considerations yield regular types. We define local versions of ℳ-rank, which also yield meager types.
4
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An essay on model theory

100%
Newelski L.
Open Mathematics
|
2003
|
tom 1
|
nr 3
398-410
EN
Some basic ideas of model theory are presented and a personal outlook on its perspectives is given.
5
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The diameter of a Lascar strong type

100%
Newelski L.
Fundamenta Mathematicae
|
2003
|
tom 176
|
nr 2
157-170
EN
We prove that a type-definable Lascar strong type has finite diameter. We also answer some other questions from [1] on Lascar strong types. We give some applications on subgroups of type-definable groups.
6
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Weak generic types and coverings of groups I

64%
Newelski L., Petrykowski M.
Fundamenta Mathematicae
|
2006
|
tom 191
|
nr 3
201-225
EN
We introduce the notion of a weak generic type in a group. We improve our earlier results on countable coverings of groups and types.
7
Content available remote

More on locally atomic models

32%
Newelski L.
Fundamenta Mathematicae
|
1990
|
tom 136
|
nr 1
21-26
8
Content available remote

A proof of Saffe's conjecture

32%
Newelski L.
Fundamenta Mathematicae
|
1990
|
tom 134
|
nr 2
143-155
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