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Axiomatizability by a schema

Published online by Cambridge University Press:  12 March 2014

Robert L. Vaught
Robert L. Vaught*
Affiliation:
University of California, Berkeley
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Extract

A theory T is axiomatizable by a schema if there is a formula Γ, involving symbols of T plus a new relation symbol R, such that the set of all (universal closures of) instances of Γ in T is a set of axioms for T. (It is understood that, if R has n places, an instance of Γ in T is obtained by properly substituting for R in Γ a formula of T which has n selected free variables and is allowed to have any number of other free variables as parameters.) Obviously, the notion is unchanged if finitely many Γ's, each involving several new R's, are allowed instead. All theories we consider are assumed to be theories in the first-order logic with equality (as in [8]), to have finitely many nonlogical symbols, and to be recursively axiomatizable.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 4 , February 1968 , pp. 473 - 479
Copyright
Copyright © Association for Symbolic Logic 1968

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References

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