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I am not sure if I understand this correctly. Please correct me.

In a formal system,

an interpretation is a mapping from its formal language to one of its structures ie models.

an formalization is a mapping from one of its models to its formal language?

So are they inverse processes to each other, in the sense that their domains and codomains are exchanged?

Thanks!

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    A formalization of, say, Group Theory cannot reasonably be viewed as a mapping from a **specific** group, say the $1$-element group, to a formal language. You may be attempting to express everything in terms of the language of sets and functions prematurely. It is useful to first get a lot of concrete experience with concrete cases.2012-02-16
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    I don't understand what you mean by a formalization.2012-02-16
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    @QiaochuYuan: I heard of that word often, such as formalize this thing and that. It sounds like some serious concept but I cant find its definition.2012-02-16
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    Not all serious concepts have an honest definition...2012-02-16

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