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Further results on infinite valued predicate logic

Published online by Cambridge University Press:  12 March 2014

L. P. Belluce
L. P. Belluce*
Affiliation:
University of California, Riverside
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Extract

In a previous paper [1] Chang and the present author presented a system of infinite valued predicate logic, the truth values being the closed interval [0, 1] of real numbers. That paper was the result of an investigation attempting to establish the completeness of the system using the real number 1 as the sole designated value. In fact, we fell short of our mark and proved a weakened form of completeness utilizing positive segments, [0, a], of linearly ordered abelian groups as admissible truth values. A result of Scarpellini [8], however, showing that the set of well-formed formulas of infinite valued logic valid (with respect to the sole designated real number 1) is not recursively enumerable indicates the above mentioned result is the best possible.

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Articles
Information
The Journal of Symbolic Logic , Volume 29 , Issue 2 , June 1964 , pp. 69 - 78
Copyright
Copyright © Association for Symbolic Logic 1964

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References

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