Model (FOL)

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Definition

For a given first order language, $\mathscr{L}$ , with a structure, $\mathbf{M}$ and an assignment, $\sigma$ , a 2-tuple (or ordered pair) $(\mathbf{M},\sigma)$ is a model of $\mathscr{L}$ ^[1].

Fully expanded a model is a tuple, $\underbrace{(\overbrace{(\underbrace{(M,\mathcal{F},\mathcal{R})}_{\text{Domain: }\mathbb{M} },\overbrace{I:\mathscr{L}\rightarrow \underbrace{(M,\mathcal{F},\mathcal{R})}_{\mathbb{M} } }^\text{Interpretation})}^\text{Structure},\underbrace{\sigma:V\rightarrow M}_\text{Assignment})}_\text{Model}$