Minimal but not strongly minimal structures with arbitrary finite dimensions

Journal of Symbolic Logic 66 (1):117-126 (2001)
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Abstract

An infinite structure is said to be minimal if each of its definable subset is finite or cofinite. Modifying Hrushovski's method we construct minimal, non strongly minimal structures with arbitrary finite dimensions. This answers negatively to a problem posed by B. I Zilber

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Citations of this work

CM-triviality and relational structures.Viktor Verbovskiy & Ikuo Yoneda - 2003 - Annals of Pure and Applied Logic 122 (1-3):175-194.
Ab initio generic structures which are superstable but not ω-stable.Koichiro Ikeda - 2012 - Archive for Mathematical Logic 51 (1-2):203-211.
A note on stability spectrum of generic structures.Yuki Anbo & Koichiro Ikeda - 2010 - Mathematical Logic Quarterly 56 (3):257-261.

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References found in this work

Stable generic structures.John T. Baldwin & Niandong Shi - 1996 - Annals of Pure and Applied Logic 79 (1):1-35.
The primal framework I.J. T. Baldwin & S. Shelah - 1990 - Annals of Pure and Applied Logic 46 (3):235-264.
An Introduction to Stability Theory.Anand Pillay - 1986 - Journal of Symbolic Logic 51 (2):465-467.

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