Can it be called a model if a sentence doesn't hold in it?

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Hill
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TL;DR
Can it be called a model if a sentence doesn't hold in it?
Consider this example:

1773696966408.webp


It seems that it is incorrect to call ##M_2## a model. Shouldn't it rather be called a structure?
 

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##M_2## is not a model of ##\Phi## but it is a model of something, so I guess it's ok.
 

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