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Construction of models from groups of permutations

Published online by Cambridge University Press:  12 March 2014

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

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
Copyright
Copyright © Association for Symbolic Logic 1975

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References

REFERENCES

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