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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Hypergraphs with finitely many isomorphism subtypes


Authors: Henry A. Kierstead and Peter J. Nyikos
Journal: Trans. Amer. Math. Soc. 312 (1989), 699-718
MSC: Primary 05C65
DOI: https://doi.org/10.1090/S0002-9947-1989-0988883-8
MathSciNet review: 988883
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Abstract: Let $ \mathcal{H} = (H,E)$ be an $ n$-uniform infinite hypergraph such that the number of isomorphism types of induced subgraphs of $ \mathcal{H}$ of cardinality $ \lambda $ is finite for some infinite $ \lambda $. We solve a problem due independently to Jamison and Pouzet, by showing that there is a finite subset $ K$ of $ H$ such that the induced subgraph on $ H - K$ is either empty or complete. We also characterize such hypergraphs in terms of finite (not necessarily uniform) hypergraphs.


References [Enhancements On Off] (What's this?)

  • [1] James E. Baumgartner, Order types of real numbers and other uncountable orderings, Ordered sets (Banff, Alta., 1981) NATO Adv. Study Inst. Ser. C: Math. Phys. Sci., vol. 83, Reidel, Dordrecht-Boston, Mass., 1982, pp. 239–277. MR 661296
  • [2] C. C. Chang and H. J. Keisler, Model theory, North-Holland, Amsterdam, 1973.
  • [3] R. Jamison, private communication.
  • [4] M. Pouzet, private communication.

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DOI: https://doi.org/10.1090/S0002-9947-1989-0988883-8
Article copyright: © Copyright 1989 American Mathematical Society