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Hometheory

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# theory

If $L$ is a logical language for some logic $\mathcal{L}$, a set $T$ of formulas with no free variables is called a *theory* (of $\mathcal{L}$). If $\mathcal{L}$ is a first-order logic, then $T$ is called a *first-order theory*.

We write $T\vDash\phi$ for any formula $\phi$ if every model $\mathcal{M}$ of $\mathcal{L}$ such that $M\vDash T$, $M\vDash\phi$.

We write $T\vdash\phi$ is for there is a proof of $\phi$ from $T$.

Type of Math Object:

Definition

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Reference

## Mathematics Subject Classification

03B10*no label found*03B05

*no label found*

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