On 10/9/2013 12:29 AM, Arturo Magidin wrote: > > Which just accomplishes the student lying to him or herself with the complicity of the professor who tells him its doable. > > Look: I don't object not telling a beginning student the whole truth; I **do** object telling him lies. > >
Let me ask you about an actual situation.
In the logic text I used as an undergraduate the notion of model had been introduced with respect to a "sentence" from a formal language.
In Chang and Keisler, models apply to languages as a whole, and, a language is a list of uninterpreted parameters as in universal algebra.
To be more clear concerning the first text, a "structure" is a "model" of a sentence if the sentence is "true with respect to a translation under the structure"
Note that this is different from "true in a model" in the sense of Chang and Keisler.
That is, a sentence may be true in a structure or a structure may be a model of a sentence.
In my naivete, the latter suggests that an admissibility criterion applied to structures could influence something like the status of an independent statement. When one speaks of a model for a language, that notion does not suggest itself.