Abstract
We prove the “Main Gap” for the class ofa-models (sufficiently saturated models) of an arbitrary stable 1-based theoryT. We (i) prove a strong structure theorem fora-models, assuming NDOP, and (ii) roughly compute the number ofa-models ofT in any given cardinality.
The analysis uses heavily group existence theorems in 1-based theories.
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References
[BH] Bouscaren, E., Hrushovski, E.: Interpreting groups in stable 1-based theories. Preprint (1992)
[EPP] Evans, D., Pillay, A., Poizat, B.: A group in a group. Algebra i Logika, vol. 3 (1990)
[H] Hrushovski, E.: Ph.D. thesis, Berkeley (1986)
[HM] Harrington, L., Makkai, M.: An exposition of Shelah's ‘Main Gap’. Notre Dame J. Formal Logic26, 139–177 (1985)
[HP] Hrushovski, E., Pillay, A.: Weakly normal groups. Proc. of Logic Colloquium '85. Amsterdam: North Holland 1987
[HPS] Hart, B., Pillay, A., Starchenko, S.: Triviality. NDOP and stable varieties. Preprint (1992)
[M] Makkai, M.: A survey of basic stability theory. Israel J. Math.49, 181–238 (1984)
[Po] Poizat, B.: Groupes stables. Nur al-Mantiq wal-Ma'rifah (1987)
[Sh] Shelah, S.: Classification theory, 2nd edn. Amsterdam: North-Holland 1991
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Authors partially supported by the NSERC, and by NSF grants DMS90-06628 and DMS92-03399
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Hart, B., Pillay, A. & Starchenko, S. 1-based theories — the main gap fora-models. Arch Math Logic 34, 285–300 (1995). https://doi.org/10.1007/BF01387509
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DOI: https://doi.org/10.1007/BF01387509