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Categoricity regained

Published online by Cambridge University Press:  12 March 2014

Erik Ellentuck
Erik Ellentuck*
Affiliation:
Rutgers, The State University, New Brunswick, New Jersey 08903
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Extract

One of the earliest goals of modern logic was to characterize familiar mathematical structures up to isomorphism by means of properties expressed in a first order language. This hope was dashed by Skolem's discovery (cf. [6]) of a nonstandard model of first order arithmetic. A theory T such that any two of its models are isomorphic is called categorical. It is well known that if T has any infinite models then T is not categorical. We shall regain categoricity by

(i) enlarging our language so as to allow expressions of infinite length, and

(ii) enlarging our class of isomorphisms so as to allow isomorphisms existing in some Boolean valued extension of the universe of sets.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 41 , Issue 3 , September 1976 , pp. 639 - 643
Copyright
Copyright © Association for Symbolic Logic 1976

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Footnotes

1

Supported by a fellowship from the Rutgers Faculty Academic Study Program.

References

REFERENCES

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