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Some forms of completeness

Published online by Cambridge University Press:  12 March 2014

P. C. Gilmore
P. C. Gilmore*
Affiliation:
Yorktown Heights, New York, U.S.A.
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Extract

By a theory is meant an applied first-order predicate calculus with at least one predicate symbol and perhaps some individual constants and function symbols and a specified set of axioms. In addition to the terms defined by means of the individual variables, constants, and function symbols a theory may also include among its terms those constructed by means of operators such as the epsilon or iota operators; that is, expressions like (εχΡ) or (οχΡ), where P is a well formed formula (wff) of the theory, may also be terms. A constant term of a theory F is then a term in which no variable occurs free. We are interested only in theories which have at least one constant term so that if a theory doesn't have any individual constants it must necessarily admit as terms expressions constructed by means of operators. A sentence of a theory F is a closed wff.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 27 , Issue 3 , September 1962 , pp. 344 - 352
Copyright
Copyright © Association for Symbolic Logic 1962

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References

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