Ab initio generic structures which are superstable but not ω-stable

Archive for Mathematical Logic 51 (1):203-211 (2012)
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Abstract

Let L be a countable relational language. Baldwin asked whether there is an ab initio generic L-structure which is superstable but not ω-stable. We give a positive answer to his question, and prove that there is no ab initio generic L-structure which is superstable but not ω-stable, if L is finite and the generic is saturated.

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10.1007/s00153-011-0263-6

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On superstable generic structures.Koichiro Ikeda & Hirotaka Kikyo - 2012 - Archive for Mathematical Logic 51 (5-6):591-600.

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References found in this work

A new strongly minimal set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
Stable generic structures.John T. Baldwin & Niandong Shi - 1996 - Annals of Pure and Applied Logic 79 (1):1-35.
Weight ω in stable theories with few types.Bernhard Herwig - 1995 - Journal of Symbolic Logic 60 (2):353-373.

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