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0-categorical tree-decomposable structures

Published online by Cambridge University Press:  12 March 2014

A. H. Lachlan*
Affiliation:
Mathematics Department, Simon Fraser University, Burnaby, British Columbia V5A IS6, Canada

Abstract

Our purpose in this note is to study countable ℵ0-categorical structures whose theories are tree-decomposable in the sense of Baldwin and Shelah. The permutation group corresponding to such a structure can be decomposed in a canonical manner into simpler permutation groups in the same class. As an application of the analysis we show that these structures are finitely homogeneous.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1992

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References

REFERENCES

[1]Baer, R., Die Kompositionsreihe der Gruppe alter eineindeutigen Abbildungen einer unendlichen Menge auf sich, Studia Mathematka, vol. 5 (1935), pp. 1517.CrossRefGoogle Scholar
[2]Baldwin, J. T. and Shelah, S., Second-order quantifiers and the complexity of theories, Notre Dame Journal of Formal Logic, vol. 26 (1985), pp. 229303.CrossRefGoogle Scholar
[3]Dixon, J., Neumann, P., and Thomas, S., Subgroups of small index in infinite symmetric groups, Bulletin of the London Mathematical Society, vol. 18 (1986), pp. 580586.CrossRefGoogle Scholar
[4]Hodkinson, I. M. and Macpherson, H. D., Relational structures induced by their finite induced substructures, this Journal, vol. 53 (1988), pp. 222230.Google Scholar
[5]Lachlan, A. H., Complete coinductive theories. I, Transactions of the American Mathematical Society, vol. 319 (1990), pp. 209241.CrossRefGoogle Scholar
[6]Lachlan, A. H., Complete coinductive theories. II, Transactions of the American Mathematical Society, vol. 328 (1991), pp. 527562.Google Scholar
[7]Schmerl, J., Coinductive ℵ0-categorical theories, this Journal, vol. 55 (1990), pp. 11301137.Google Scholar
[8]Schreier, J. and Ulam, S., Über die Permutationsgruppe der natürlichen Zahlenfolge, Studia Mathematka, vol. 4 (1933), pp. 134141.CrossRefGoogle Scholar