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Constructing $\omega $-stable structures: Computing rank

Tom 170 / 2001

John T. Baldwin, Kitty Holland Fundamenta Mathematicae 170 (2001), 1-20 MSC: Primary 03C60. DOI: 10.4064/fm170-1-1

Streszczenie

This is a sequel to [1]. Here we give careful attention to the difficulties of calculating Morley and $U$-rank of the infinite rank $\omega $-stable theories constructed by variants of Hrushovski's methods. Sample result: For every $k< \omega $, there is an $\omega $-stable expansion of any algebraically closed field which has Morley rank $\omega \times k$. We include a corrected proof of the lemma in [1] establishing that the generic model is $\omega $-saturated in the rank 2 case.

Autorzy

  • John T. BaldwinDepartment of Mathematics, Statistics
    and Computer Science
    University of Illinois at Chicago
    M//C 249
    851, S. Morgan St.
    Chicago, IL 60607, U.S.A.
    e-mail
  • Kitty HollandDepartment of Mathematics
    Northern Illinois University
    DeKalb, IL 60115, U.S.A.
    e-mail

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