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Omitting types of prenex formulas

Published online by Cambridge University Press:  12 March 2014

C. C. Chang
C. C. Chang*
Affiliation:
University of California, Los Angeles
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Extract

In the literature, a type Γ is a set of formulas ϕ(ν0) in the one free variable ν0. A model M realizes Γ if there is an element a of M such that

M ╞ ϕ [a] for all ϕ ∈ Γ.

A model M omits Γ if no element of M realizes Γ. Evidently, the two statements:

(*) M realizes Γ

and

(**) M omits Γ

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 1 , June 1967 , pp. 61 - 74
Copyright
Copyright © Association for Symbolic Logic 1967

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References

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