Abstract
We construct an ab initio generic structure for a predimension function with a positive rational coefficient less than or equal to 1 which is unsaturated and has a superstable non-ω-stable theory.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baldwin, J.T.: Problems on pathological structures. In: Wolter, H., Weese, M. (eds.) Proceedings of 10th Easter Conference in Model Theory, vol. 1993, pp. 1–9 (1993)
Baldwin, J.T.: A field guide to Hrushovski’s constructions, slides of a survey talk available at http://www.math.uic.edu/~jbaldwin/pub/hrutrav.pdf (2009)
Baldwin J.T., Shi N.: Stable generic structures. Ann. Pure Appl. Log. 79, 1–35 (1996)
Hrushovski, E.: A stable \({\aleph_0}\) -categorical pseudoplane (preprint) (1988)
Hrushovski E.: A new strongly minimal set. Ann. Pure Appl. Log. 62, 147–166 (1993)
Ikeda K.: Ab initio generic structures which are superstable but not ω-stable. Arch. Math. Log. 51, 203–211 (2012)
Ikeda K.: A note on strictly superstable generic structures (in Japanese). Kokyuroku RIMS 1741, 1–8 (2011)
Ikeda K., Kikyo H., Tsuboi A.: On generic structures with a strong amalgamation property. J. Symb. Log. 74(3), 721–733 (2009)
Wagner F.O.: Relational structures and dimensions. In: Automorphisms of First-order Structures, pp. 153–181. Clarendon Press, Oxford (1994)
Wagner F.O.: Fields and fusions, Hrushovski constructions and their definable groups. Kokyuroku RIMS 1718, 27–40 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ikeda, K., Kikyo, H. On superstable generic structures. Arch. Math. Logic 51, 591–600 (2012). https://doi.org/10.1007/s00153-012-0284-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00153-012-0284-9