# zbMATH — the first resource for mathematics

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
Full Text:
##### References:
 [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.