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Construction of models from groups of permutations

Published online by Cambridge University Press:  12 March 2014

Miroslav Benda
Miroslav Benda*
Affiliation:
University of Washington, Seattle, Washington 98195
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Extract

In [3] we have associated to a structure an ordinal which gives us information about elementary substructures of the structure. For example a structure whose ascending chain number (as we call the ordinal) is ω could be called Noetherian since all ascending elementary chains inside it are finite (and there are arbitrarily large finite chains). Theorem 2 shows that such structures exist. In fact we prove that for any α < ω1 there is a structure whose ascending chain number is α. The construction is based on the existence of a certain group of permutations of ω (see Theorem 1). The second part of this paper deals with the relevance of the chain number to the study of Jonsson algebras.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 40 , Issue 3 , September 1975 , pp. 383 - 388
Copyright
Copyright © Association for Symbolic Logic 1975

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References

REFERENCES

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