A note on generic projective planes. (English) Zbl 1050.03025

Summary: E. Hrushovski (1988) constructed an \(\omega\)-categorical stable pseudoplane which refuted Lachlan’s conjecture. In this note, we show that an \(\omega\)-categorical projective plane cannot be constructed by “the Hrushovski method.”


03C45 Classification theory, stability, and related concepts in model theory
03C35 Categoricity and completeness of theories
Full Text: DOI


[1] Baldwin, J. T., ”Problems on ‘pathological’ structures”, pp. 1–9 in Proceedings of the Tenth Easter Conference on Model Theory , edited by M. Weese and H. Wolter, vol. 93 of Seminarberichte , Humboldt Universität Fachbereich Mathematik, Berlin, 1993. · Zbl 0798.03035
[2] Baldwin, J. T., ”An almost strongly minimal non-Desarguesian projective plane”, Transactions of the American Mathematical Society , vol. 342 (1994), pp. 695–711. · Zbl 0796.03041
[3] Baldwin, J. T., and N. Shi, ”Stable generic structures”, Annals of Pure and Applied Logic , vol. 79 (1996), pp. 1–35. · Zbl 0857.03020
[4] Cameron, P. J., Oligomorphic Permutation Groups , vol. 152 of the London Mathematical Society Lecture Note Series , Cambridge University Press, Cambridge, 1990. · Zbl 0813.20002
[5] Cherlin, G., L. Harrington, and A. H. Lachlan, ”\(\aleph_ 0\)”-categorical, \(\aleph_ 0\)-stable structures, Annals of Pure and Applied Logic , vol. 28 (1985), pp. 103–35. · Zbl 0566.03022
[6] Hodges, W., Model Theory , vol. 42 of Encyclopedia of Mathematics and its Applications , Cambridge University Press, Cambridge, 1993. · Zbl 0789.03031
[7] Hrushovski, E., ”A stable \(\aleph_0\)-categorical pseudoplane”, preprint, 1988.
[8] Wagner, F. O., ”Relational structures and dimensions”, pp. 153–80 in Automorphisms of First-Order Structures , Oxford University Press, New York, 1994. · Zbl 0813.03020
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.