(Model theorists say that such a sentence is fully interpreted).
Model theorists use them as a way of building infinite structures with controlled properties.
In practice model theorists often draw themselves pictures of structures, and use the pictures to think about the structures.
This is the view of Martin (1998), Steel (2000), Woodin (2005a), many philosophers and mathematicians, and most descriptive set theorists and inner model theorists.
These models are known as Ehrenfeucht-Mostowski models, after the two Polish model theorists who first carried out this construction in the mid 1950s.
Since ⊨ and ⊢ express exactly the same relation in this case, model theorists often avoid the double use of ⊨ by using ⊢ for model-theoretic consequence.
Some critics accuse social model theorists of assuming that any disadvantage caused by the social environment is ipso facto unjust (Samaha 2007).
But most model theorists are uncomfortable with any kind of division by zero, so they stick with plus, times and minus.
But since the line of argument set out in the previous paragraph simply ignores the mode of phenomenal unity posited by Extensional model theorists, it fails to provide us with any reason for thinking this is the case.
This aspect of Frege's logic, however, remained in the background for a long time, and model theorists in the 50s and 60s seem not to have been aware of it.
