User:IssaRice/Computability and logic/Semantic completeness

Semantic completeness is sometimes written as: if $T\models \phi$ , then $T\vdash \phi$ .

Semantic completeness differs from negation completeness.

Definition

Smith's definition: a logic is semantically complete iff for any set of wffs $\Sigma$ and any sentence $\phi$ , if $\Sigma \models \phi$ then $\Sigma \vdash \phi$ .^[1]

↑ Peter Smith. An Introduction to Godel's Theorems. p. 33.

[1] Peter Smith. An Introduction to Godel's Theorems. p. 33.

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