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A new strongly minimal set. (English) Zbl 0804.03020
Summary: We construct a new class of \(\aleph_ 1\) categorical structures, disproving Zilber’s conjecture, and study some of their properties.

MSC:
03C35 Categoricity and completeness of theories
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[1] Baldwin, T.J.; Lachlan, A., On strongly minimal sets, J. symbolic logic, 36, 79-96, (1971) · Zbl 0217.30402
[2] Cherlin, G.; Harrington, L.; Lachlan, A., ℵ_0-categorical ℵ0-stable structures, Ann. pure appl. logic, 18, 227-270, (1980) · Zbl 0566.03022
[3] Fraissé, R., Sur l’extension aux relations de quelques propriétés des ordres, Ann. sci. école norm. sup., 71, 361-388, (1954) · Zbl 0057.04206
[4] E. Hrushovski and J. Loveys, Locally modular strongly minimal sets, to appear. · Zbl 1197.03040
[5] Hrushovski, E.; Pillay, A., Weakly normal groups, The Pan’s logic group, (1987), North-Holland Amsterdam, Logic Colloquium ’85 · Zbl 0636.03028
[6] E. Hrushovski, Interpreting groups in homogeneous geometries.
[7] Hrushovski, E., Unimodular strongly minimal sets, London J. math, 46, 2, 365-396, (1992)
[8] Hrushovski, E., Unidimensional theories, () · Zbl 0713.03015
[9] Hrushovski, E., Almost orthogonal regular types, Ann. pure appl. logic, 45, 139-155, (1989) · Zbl 0697.03023
[10] Hrushovski, E.; Shelah, S., A dichotomy theorem for regular types, Ann. pure appl. logic, 45, 157-169, (1989) · Zbl 0697.03024
[11] E. Hrushovski and G. Srour, A non-equational stable theory, Preprint.
[12] Laskowski, M., Doctoral dissertation, (1986), Berkeley
[13] Morley, M., Categoricity in power, Trans. am. math. soc., 114, 514-538, (1965) · Zbl 0151.01101
[14] Pillay, A., Stable theories, pseudoplanes and the number of countable models, Ann. pure appl. logic, 43, 147-160, (1989) · Zbl 0676.03024
[15] Pillay, A.; Srour, G., Closed sets and chain conditions in stable theories, J. symbolic logic, 49, 1350-1362, (1984) · Zbl 0597.03018
[16] Zilber, B., Strongly minimal countably categorical theories II-III, Siberian math. J., 25, 396-412, (1984) · Zbl 0581.03022
[17] Zilber, B., Strongly minimal countably categorical theories II-III, Siberian math. J., 25, 559-571, (1984) · Zbl 0599.03031
[18] Zilber, B.I., Strongly minimal countably categorical theories, Siberian math. J., 21, 219-230, (1980) · Zbl 0486.03017
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