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Nonstandard logic

Published online by Cambridge University Press:  12 March 2014

James R. Geiser
James R. Geiser*
Affiliation:
Dartmouth College
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Extract

This paper is an exposition of the author's [2] investigations of a class of infinitary first order logics. These logics are sometimes characterized by saying that the syntactical role played by the positive integers in first order predicate logic is taken over by a nonstandard model of arithmetic. The result is then called a nonstandard logic.1 In particular the operations of conjunction, disjunction and quantification may be iterated infinitely (nonstandard finitely) often.

When the nonstandard model of arithmetic is an ultra power, the natural class of structures in which to interpret the nonstandard wffs is a class of ultra products. Within this framework, many model-theoretic properties of ultra products become manifest in the logical structure of the nonstandard language.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 2 , 23 July 1968 , pp. 236 - 250
Copyright
Copyright © Association for Symbolic Logic 1968

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References

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