Model Theory and Forgetful Functor
Oct. 30th, 2016 10:45 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
timeletsGoing back to the conversation about forgetful functors.
Stanford Encyclopedia of Philosophy on Model Theory:
Whenever we see a statement S we can assume that it is missing the I portion. In short, the agent created a mapping from SxI to S, using a forgetful functor F: SxI -> S.
Right?
When I say "любой переход к модели - это forgetful functor" I mean that, to figure out the model I for S we have to figure out F. Most likely, my original statement is incorrect in mathematical sense.
Stanford Encyclopedia of Philosophy on Model Theory:
Sometimes we write or speak a sentence S that expresses nothing either true or false, because some crucial information is missing about what the words mean. If we go on to add this information, so that S comes to express a true or false statement, we are said to interpret S, and the added information is called an interpretation of S. If the interpretation I happens to make S state something true, we say that I is a model of S, or that I satisfies S, in symbols ‘I ⊨ S’. Another way of saying that I is a model of S is to say that S is true in I, and so we have the notion of model-theoretic truth, which is truth in a particular interpretation.
Whenever we see a statement S we can assume that it is missing the I portion. In short, the agent created a mapping from SxI to S, using a forgetful functor F: SxI -> S.
Right?
When I say "любой переход к модели - это forgetful functor" I mean that, to figure out the model I for S we have to figure out F. Most likely, my original statement is incorrect in mathematical sense.
