# What does the following mean for sets?

What does the following mean in terms of sets? Can someone explain this in words?

$$\{x \mid I \vDash \varphi(x)\}$$

where $I$ is an interpretation

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## 2 Answers

All $x$ such that $\varphi(x)$ is true in this interpretation.

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$\{x \mid I \vDash \varphi(x)\}\;\;$ is the set of all $\;x\;$ such that $\;\varphi(x)\;$ is true in the given interpretation $I$.

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