Abstract
We outline the structure theory for infinite structures which are smooth limits of finite structures, or equivalently for sufficiently large finite permutation groups with a bounded number of orbits on 4-tuples. The primitive case is treated explicitly in [11] assuming a bound on orbits on 5-tuples, and modifications needed to work with a bound on 4-tuples are indicated in [15]. This theory is an extension of the theory of ℵo-categorical ℵo-stable structures. The main technical innovations at this level of generality are due to Hrushovski; some of them are useful in other semistable contexts.
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© 1997 Springer Science+Business Media Dordrecht
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Cherlin, G. (1997). Large Finite Structures with Few Types. In: Hart, B.T., Lachlan, A.H., Valeriote, M.A. (eds) Algebraic Model Theory. NATO ASI Series, vol 496. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8923-9_3
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DOI: https://doi.org/10.1007/978-94-015-8923-9_3
Publisher Name: Springer, Dordrecht
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