A+ CATEGORY SCIENTIFIC UNIT

m-normal theories

Volume 170 / 2001

Ludomir Newelski Fundamenta Mathematicae 170 (2001), 141-163 MSC: Primary 03C45. DOI: 10.4064/fm170-1-9

Abstract

Originally, m-independence, ${\cal M}$-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 $<2^{\aleph _0}$ countable models is m-normal. In particular, any $*$-algebraic group interpretable in such a theory is abelian-by-finite.

Authors

  • Ludomir NewelskiMathematical Institute
    Wroc/law University
    50-384 Wroc/law, Poland
    and
    Mathematical Institute
    Polish Academy of Sciences
    51-617 Wroc/law, Poland
    e-mail

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