What does the following mean for sets?

Question

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

Matt N. · Answer 1 · 2012-12-06 19:28:03Z

up vote 1 down vote

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

answered Dec 6 '12 at 19:28

Matt N.
15.3k32270

amWhy · Answer 2 · 2012-12-07 03:36:04Z

up vote 1 down vote

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

edited Dec 7 '12 at 3:36

answered Dec 6 '12 at 21:42

amWhy
55.3k774157

2 Answers