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Constructing \(\omega\)-stable structures: rank \(k\)-fields. (English) Zbl 1071.03020
Summary: Theorem: For every \(k\), there is an expansion of the theory of algebraically closed fields (of any fixed characteristic) which is almost strongly minimal with Morley rank \(k\).
MSC:
03C45 Classification theory, stability, and related concepts in model theory
03C35 Categoricity and completeness of theories
03C60 Model-theoretic algebra
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[1] Baldwin, J. T., and K. Holland, “Constructing \(\omega\)-stable structures: Rank 2 fields,” The Journal of Symbolic Logic , vol. 65 (2000), pp. 371–91. JSTOR: · Zbl 0957.03044
[2] Baldwin, J. T., and K. Holland, ”Constructing \(\omega\)”-stable structures: Computing rank, Fundamenta Mathematicae , vol. 170 (2001), pp. 1–20. Dedicated to the memory of Jerzy Ł oś. · Zbl 0994.03030
[3] Holland, K. L., ”Model completeness of the new strongly minimal sets”, The Journal of Symbolic Logic , vol. 64 (1999), pp. 946–62. JSTOR: · Zbl 0945.03045
[4] Pillay, A., An Introduction to Stability Theory , vol. 8 of Oxford Logic Guides , The Clarendon Press, New York, 1983. · Zbl 0526.03014
[5] Poizat, B., Groupes Stables. Une Tentative de Conciliation Entre la Géométrie Algébrique et la Logique Mathématique , vol. 2 of Nur al-Mantiq wal-Ma’rifah [Light of Logic and Knowledge , Bruno Poizat, Lyon, 1987. · Zbl 0633.03019
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